I am not sure exactly what you want. Edward is an old Christian name.
This is what Ancestry.Com has about Lewis

Lewis Name Meaning English (but most common in Wales): from Lowis, Lodovicus, a Norman personal name composed of the Germanic elements hlod 'fame' + wig 'war'. This was the name of the founder of the Frankish dynasty, recorded in Latin chronicles as Ludovicus and Chlodovechus (the latter form becoming Old French Clovis, Clouis, Louis, the former developing into German Ludwig). The name was popular throughout France in the Middle Ages and was introduced to England by the Normans. In Wales it became inextricably confused with 2.Welsh: from an Anglicized form of the personal name Llywelyn (see Llewellyn).Irish and Scottish: reduced Anglicized form of Gaelic Mac Lughaidh 'son of Lughaidh'. This is one of the most common Old Irish personal names. It is derived from Lugh 'brightness', which was the name of a Celtic god.Americanized form of any of various like-sounding Jewish surnames.

Source: Dictionary of American Family Names ©2013, Oxford University Press

Taylor is an occupational name. One of the ways people took surnames is their occupation became their surname.

Mary, you don't want to start out on the internet anyway. Oh the internet can be a useful tool. You start with yourself and work back one generation at a time, documenting everything as you do.

First find out what living family might have. Maybe they have some birth, marriage and death certificates on ancestor, old photos, family bibles, wills, deeds etc. Depending on the religious faith of your ancestors, baptismal, confirmation, marriage and death records from their churches can be just as helpful if not more so than civil records. Maybe family members have certificates on your ancestors from their churches.

Interview your senior family members and tape them if they will let you. Chances are they will get into telling stories of days gone by you wouldn't write down but in those stories frequently are clues that will help you break through a brick wall in your research. You should go back and listen to the tapes while doing research as you will probably hear things you didn't hear the first time around. Now not all family stories turn out to be accurate but you should get them anyway.

Go to a Family History Center at a Latter Day Saints(Mormon) Church. They have records on people all over the world, not just Mormons. If you find anything in their database you would like to view and print off a copy of an original document, they can order microfilm for you to view for a reasonable fee. I have never had them to try and convert me nor have I heard of them doing that to anyone else that has used their resources. A lot of their volunteers are not Mormon. Just use the following link to find the nearest Mormon FHC.

https://familysearch.org/locations/

Find out what you public library has in genealogy.

Once you have done some preliminary work then using the internet as a tool can be helpful. You would have a better idea as to what you need to be searching.

Do not take as fact what you see in family trees on ANY website, free or fee without verifying it with actual documents. The trees are submitted by the subscribers to the website not some experts who take it upon themselves to willy nilly trace the ancestry of other people. Yes, there are errors. Even when you see the exact same information on the same people from a multitude of other subscribers that doesn't mean it is correct as too many people copy without verifying. Actually if you just happen to find any of your ancestors in an online tree and you see information you know is wrong, those that run the website will tell you that is between you and the other subscriber. They don't get involved, It would be far too costly for them to hire people to verify all the information their subscriber submit.

There are 2 that each probably have more records online than any of the others. They also have family trees. Just distinguish the difference between the records they have and their subscriber submitted family trees. One is Ancestry.Com which many public libraries have a subscription to you can use for free. The other is entirely free. It is FamilySearch.org. Now, no way are all records online. Many times they have the images of the original document but when they don't the fee for writing an obtaining a copy of the original document is far less than travleling, maybe 2000 miles to the particular courthouse to get it.

Surnames are not proof or even an indication of ancestry. The only thing you can do is research your ancestry.

Surnames were taken in Europe during the last millennium. Originally they weren't to identify a person as a member of a family but just to better identify, frequently for taxation purposes. There were too many men with the same given name, i.e. John, William, Robert, Thomas etc, and they just had to have a way of sorting them all out. When they got through it wasn't impossible for legitimate sons of the same man to wind up with a different surname and still each could have shared his with others with no known relationship.

Ancestry.Com has this about Whaley.

Whaley Name Meaning English: habitational name from Whaley in Derbyshire, Whalley in Lancashire, or Whaley Bridge in Derbyshire (formerly in Cheshire). The first is probably named with Old English wælla 'spring', 'stream' + leah '(woodland) clearing'. The second has as the first element Old English hwæl 'round hill', and the last has Old English weg 'path', 'road' as the first element, the second element in both cases also being leah.

Source: Dictionary of American Family Names ©2013, Oxford University Press

So you can see if could have been applied to a lot of people not necessarily related.

Well if you hold a French passport you are definitely a French citizen.

As you were born in the UK after 1 Jan 1983, you are British if one of your parents was British or held indefinite leave to remain at the time of your birth. Since your father is British, as long as your parents were married (until July 2006 only fathers of legitimate children could pass on citizenship), you are also a British citizen. It's up to you whether you choose to exercise that citizenship by applying fr a British passport or not.

Did your mother acquire any other nationality before your birth? If so, she lost her Armenian citizenship as until recently dual citizenship was not recognised. This would mean that you could have no claim to Armenian citizenship. If your mother remained an Armenian citizen you have a claim to that citizenship as well. Again, whether you choose to exercise it is your choice.

There is nothing to stop you holding all three passports if you wish and choosing to travel as either a British, French or Armenian citizen. Of course if you choose to travel within the EU as an Armenian you would be subject to immigration control as Armenians do not have the right of free movement in the EU. Also remember that the passport that you use to enter a country determines what consular assistance you can ask for if you get into trouble, are a victim of crime or lose your passport etc.

Lucy, be extremely cautious about taking as absolute fact anything you see in family trees on their website or any website. The trees are submitted by the subscribers to the website and yes, there are errors. Even when you see the absolute same information on the same people from a ton of other subscribers that doesn't mean it is accurate as too many people copy without verifying with actual records. Actually if you have found any of your family in one of their online trees and you happen to see something you know is wrong, those that run the website will tell you that is between you and the other subscriber. They don't get involved. It would cost them a fortune to hire people to verify all the information their subscriber submit.

Now Ancestry.Com and a free website, FamilySearch.org each probably have more records than any of the other websites. That no way means all records are online. When you find records on your family you should get a copy of the original document from the courthouse, state library or whatever.

Now, if you haven't done so you should get as much information from living family as possible. Find out who just might have some birth, marriage and death certificates on your ancestors, wills, deeds, etc. Also maybe some family has some old family bibles. Depending on the religious faith of your ancestors, baptismal, confirmation, marriage and death records from their churches can frequently be just as helpful if not more so than civil records. Maybe some of your family have certificates on your ancestors from their churches.

Interview your senior family members and tape them if they will let you. Chances are they will get into telling stories of days gone by you wouldn't write down but frequently in those stories are clues that will help you break through a brick wall in your research. You should go back periodically and listen to the tapes again while doing research as you probably will hear things you didn't hear the first time around. Not all family stories pan out but you should get them anyway.

I might add no DNA test will tell you who your specific ancestors were and DNA test in isolation of traditional genealogy using documents and records is really a big waste of money.