Long time lurker here - might not be of use for you but hey i'll chime in and then be told im wrong by someone but that's what the forum is here for
I'm only talking from personal experience and how I play and what I've been coached over the years.
1. Should a batsman have different technique for different types of bowling? Eg: Swing v/s spin?
You can do and I certainly do, whether you should do? I'd say yes probably based on watching a lot of professional cricket, I think it would be fair to say most players do with an extreme example being Ben Foakes. I know I use a bigger stride when facing spin on the front foot and when playing spin off the back foot (unless im cutting the ball late) I square myself up more than I would playing a seamer off the back foot.
2. Can you use same technique to defend v/s power-hit a ball to another dimension? Reason I ask this is because there is some pre-meditation in my power shots.
I think the basis of a strong base still needs to be there in whatever you are trying to do. But personally I know my technique changes slightly when hitting compared to when defending a ball, for one i'll go long through the ball rather than slowing the bat down into contact. I also pre meditate some power shots but find its knowing when it isn't quite there to reign it in and play the ball differently.
3. Off-cutters at good length that get thru my defence
This would suggest to me that you are playing round the ball so bat isn�t coming down straight thus leaving a gap - I'll copy
@roco 's response for this one.
4. I have been squared up by out-swingers pitching middle/leg and then barely missing my off stump. I have noticed that at close range, any sharp change in direction whether it is seam or swing is nearly impossible to track by my eyes. If I am anticipating that movement, then I can track it. If I am not ready for it, that (near) lateral movement is so quick that my eyes can't track it. What's the best approach for that?
But the ball has missed off stump? You are still there
if it has done that then fair play to the bowler. There are some cases when you will pick up the movement and be able to adjust, occasions when it will just move and wont have time to adjust and the ones in the middle, you'll see it move and have some time to adjust but not quite enough. In these i'd say back your technique and dont follow it, times when I have followed it have just led me to snick off. Bowlers are allowed to bowl good balls ( it really pains us bats to say that) but if you look at your dismissals for a season there are going to be some that you just couldn't avoid, its the rest of them that you want to try and remove from your game.
Apologies for the long one - just fancied chiming in for once.