How to open from button heads up pre flop?
That's up to your strategy, really. In heads-up matches, keeping in mind that you play deep-stack, it is common practice to play a wide range of hands in position. This way you apply huge pressure to your opponent, because in order to defend he needs a) either to call wider and play lots of hands out of position (this will give you a great advantage post-flop, lots of value from your value-hands and advantage when you are bluffing) OR b) re-raise wider (in that case your min-raise is your ally, since you don't commit a lot of money).
It seems like there is almost no fold equity.
In fact, mathematically it is true that there is little to no fold equity. But you need to consider other factors as well, like reverse implied-odds. When you play deep and you hold something like Q-4, you do have enough equity against your opponent range (assuming he opens wide). However, remember that you don't go all in preflop. You need to think of post game. Since you are deep, you will end-up facing a potential of three barells. Even if your Queen hits, he could hold something like Q-9 and just with that lousy hand he will extract lots of value.
How to bet if re-raised?
Again, a big topic of discussion. There is no default strategy. It depends of many factors. If you choose to play the wide strategy you mentioned before, you have to expect lots of re-raises from your opponent, thus you need to defend against his strategy. Since you are deep, you can choose a range of strong hands to call his reraises and defend in position (hands like KQs, AJs, T9s, even AK), some very strong hands to 4-bet like AA,KK,QQ and some lousy hands to bluff. This could be a balanced strategy in general terms, quite polarized, but viable in small and mid-stakes. The amount of your 4-bet is pretty standard (around 2x to 2.5x the amount of 3-bet, unless you get commited, where you need to shove).
Examples:
1) Player A, B (effective 100 BB)
A raises to 2
B 3bets to 6
A 4bets to 15...18 (you are quite deep so you can 4bet larger)
2) Player A,B (eff. 50 BB)
A raises to 2.5
B 3bets to 7
A 4bets to 14...17 (here you go for a min-4-bet given lower stacks)
3) Player A,B (eff. 30 BB)
A raises to 2
B 3bets to 7
A 4bets shoves (you cannot just bet 14, you are committed already, so shove)