Ill join the chorus saying that you shouldnt worry about your name being lore-appropriate. Most people wont question it, and if it starts to come up in your social circles you can put together a backstory to cover it. Your race ranking is off though. It goes Elezen at the very top, then miquote, then hyur/au ra, then much further down lala, and at the very bottem roe's. On to the questions.
Favorite thing? Story. Where its been, and where its going. I cant answer your endgame question, because i dont feel like ive done everything yet.
Dos:
Keep a quest from the main scenario in your journal all the time. Even if you plan to take a break from advancing the story, always pick up the next MSQ quest before you stop. If you dont it can sometimes be tough to remember where you were when you need to start back up again.
Try different classes. The freedom to be everything is worth embracing at least partly. Not saying you need to do everything, but for sure try a few different things.
Explore the world. There are a ton of things you can miss if you just rush to the end game. So look around, and find some of them.
Donts:
Stress out about your gear. While leveling up, you can get away with replacing your armor every 10-15 or so levels. Your jewelry can go longer then that(there arent as many jewelry upgrades). So dont worry if your stuff is a few levels old. If you feel under-powered, your weapon makes the biggest difference so upgrade that first.
Be afraid to try out crafting and gathering. Crafting and gathering in this game are treated very differently then they are in most other MMOs. So try em out. They can make you extra money, they can let you upgrade and repair your own gear, and they can give you an extra thing to do if you arent in a questing/killing mood.
Be afraid to ask for help. There are plenty of things in the game that arent obvious. If you need help with something please ask. Here on the boards, in game with your FC/LS members, wherever.
Bonus Do: Have fun. Duh.