The Duchy of Somerset is one of the most prestigious in England, second in precedence only to the Dukes of Norfolk and the Royal Family in the peerage of the UK. However, ducal titles typically are not passed through the female line in England.

The only major exception that I am aware of is the Duchy of Marlborough, which has been able to be passed down in the female line since a 1706 Act of Parliament. English general John Churchill was made 1st Duke of Marlborough for his services in the War of the Spanish Succession (1701-1714). The national hero died without a male heir, and his wife was a personal friend of Queen Anne, and it was decided that his title should not be allowed to go extinct so soon (though his lesser titles did). Churchill's daughter Henrietta became Duchess of Marlborough in her own right, and passed the title along to her nephew.

Unfortunately, I have no advice for you regarding tracing ancestry. Sorry!

Titles are almost never passed to female offspring. If there is no male offspring then the title is allowed to die. In addition if your parents don't have titles then you don't either unless the queen give you one.

Here's a screenshot of a page in the book Medieval Underpants and Other Blunders: A Writer's (& Editor's) Guide to Keeping Historical Fiction Free of Common Anachronisms, Errors, & Myths, using Downton Abbey as an example to explain female offspring of nobility. basically Robert Crawley, Earl of Gratham is married to Cora Crawley, Countess of Gratham. Their daughters are called Lady ___ Crawley, without the title of countess. Their children get no title unless their father has a title.

Concerning your ancestry, you can start by having a look there --> /r/genealogy

Just use the search bar by mentioning your country.

Just a tip, most people who are doing research on their family history ( thus searching their ancestors ) need to start on the bottom of the tree, meaning you ( or you children for example ) but not someone who lived three centuries ago. Unless of course you are doing specific research on this person's descendants ( pretty useless if the purpose is to connect it to you ).

You can just have a look at /r/genealogy. Just take a look at previous topics before asking about how to start as I am sure there have been plenty of people who already asked about how to get started and received great answers. Good luck ;)