Shakespeare.
Become a good player of an instrument of your choosing or a true virtuoso in an instrument of my choosing (no hints)?
You choose (but now you have to tell me). I’ll try to build a performing career around it somehow.
Shrimp cocktail or scampi?
Scampi. Cold shrimp aren’t my thing.
Would you rather eat Chinese hot mustard or ghost peppers?
Vibraphone. Off you go!
Definitely hot mustard. Not nearly as many hospitalizations with that stuff.
Spend four years in a Trump America or one year in Somalia?
Somalia; I like travel abroad.
8 years of President Trump, or 12 years of President Cruz-then-Pence-then-Rubio?
Cruz-Pence-Rubio
Would you rather know who let the dogs out, or who DID kill the deputy?
:: grits teeth ::
OK, this might take awhile.
In play:
The deputy. I already know the answer to the first: http://jokideo.com/wp-content/uploads/2012/03/428595_274462069294509_126894987384552_630989_2125997425_n.jpg
Next:
Visit Tokyo or Beijing?
Tokyo.
PhD in Physics or Chemistry?
Physics.
Oscar of your choosing or Olympic Gold Medal in your favorite sport?
An Oscar, definitely. And can I see that it’s awarded to someone other than me? Because Bradley Cooper should’ve won it for Best Actor in Limitless.
Dinner with Bradley Cooper or Robert De Niro?
Bradley Cooper seems much more interesting.
Star in an off-Broadway musical written by nobodies but that looks promising, or have a minor role in a movie based on a best selling book directed by and starring major talents?
Minor role. I even know which one. 
Direct an episode of your favorite TV show or sing karaoke with your favorite musician?
Sing ~with Patsy Cline ~ Would you rather loose your sense of smell or taste?
Well, if your sense of smell goes, so goes your sense of taste. So I guess taste. At least I could still smell stuff!
Babysit for an infant or a toddler?
A toddler. He or she can at least tell you where he or she hurts.
Be 21 again, or have millions of dollars?
ETA: I have no sense of smell. I can still taste fine.
Assuming I get to take my memories and knowledge with me, I’ll be 21 again.
Give up riding in cars forever or eat only from 7-11 for the rest of your life?
Riding in cars. I mostly walk or take buses anyway.
Inherit Trump’s fortune if you let him be President for eight years, or inherit the Clinton’s fortune but don’t let her be President.
Either of those, practically speaking, means I’ll be stuck with a President Trump, which sucks. I guess I’ll go with Option B, since at least that doesn’t guarantee him eight years in office (and - bonus! - I get all of Hillary’s money).
In ten years, Moon colony or manned Mars landing?
Mar’s ~~many Earthly similarities would you rather work on a fishing fleet out of Alaska or drive semi truck in Alaska?