As comfortable as I'd be with a woman taking contraceptives. None are completely safe and there haven't been nearly enough studies on their effects (particularly the mental health implications).
Just because there hasn't been enough study on men's birth control, doesn't mean we put the burden of contraceptives on women alone.
When it has an issue of effectiveness you usually can tell pretty quick
Whereas medication (at least in my experience) can suddenly stop being as effective due to your body building a tolerance, something you ate, an allergy forming that wasn't there before, etc.
Probably not, I'd likely stick with condoms. Any male contraceptive medication would be too new to have any clear idea of whether it was safe. Even for women's contraceptives that have been around for decades, there are a ton of potential side effects and risks.
A male contraceptive medication would have to work through a fundamentally different mechanism than female birth control, requiring changes to sperm or sperm production. I myself would be extremely skeptical until it had been on the market for a long period of time. This is less a skepticism of science and more of a skepticism of the pharmaceutical industry (particularly in the states).
Edit: After looking into the mechanisms of the up and coming methods (primarily hormonal) that have been in the news I think my conclusion was a little hasty. I think long term risks are likely very low or at least comparable to women's birth control.
I think calling it male contraception would make it weird for me because i am not male/a man. Still, I would have definitely used in the past, but know i dont need it any more.