I plan to get a trademark registered and I was searching the USPTO website to see if it already taken or not. I figured out the Live/Dead Indicator is "Dead". Does that mean I can get this trademark?
Also--if I own a trademark, and the domain of that trademark is taken by some other person, can I ask them to give it to me on the grounds that I am the legitimate owner of the trademark?
usually the reason a trademark is 'dead' is because it could not be trademarked in the first place. Trademarks can only be applied in very specific circumstances and say for example you want to trademark "Comfy Soft Mattress" as a trademark you will find that you can't because the name is also a description of the product. Many people fall into that trap.
Also no you can't get the website because you would need to prove that the person deliberately registered it to profit from your name ... as it sounds like you don't even really exist yet I can't see that you would be successful.
By the way, just trading with the name means you have rights to the name (or the true trademark holder having rights to sue you). No need for registration
seek advice from an IM lawyer or Trademarkia for help in this area, mostly it comes down to choosing a new and unique name before going forward with registration if you so choose to