I agree with you that people will continue to think Braun did it no matter what, because that's the kind of doubt this entire situation has sown. But I would like to add that Braun made his leap in production at age 27, the age most in baseball consider to the beginning of players' primes.
He also didn't really have too much of a leap in production. Outside of stealing a lot more bases, his numbers were pretty much in line with his career - slightly above average, but nothing unusual. If he did do steroids just this season, they weren't particularly effective. It's also a bit of a weird thing to do just after cashing in on a huge long-term contract - the upside seems limited since you're not going to get any extra money by being great anytime soon (he's signed through 2020). 2018-2020 seems to be the time to try it, if anything.
Absolutely possible. But he's passed something like 20 drug tests, I think. So either he used very sporadically, used something that masks it really well, or the drug tests suck.