One advantage of wavedashing is that it requires jumping, which you can do in many more situations than you're free to run. You can jump, and therefore wavedash, while shielding, dashing, running, crouching, and you can do any ground action out of it, whereas while running you can only shield, dash attack, crouch, or jump. It's a very quick way to get off a platform or move off the edge backward (either to be able to use the correct aerial or be able to grab the ledge). It's a very versatile technique; there are more uses than I can reasonably list.
Tech skill is something you practice. There is no trick. You have to develop muscle memory. To learn to wavedash, wavedash. To learn to SHFFL, short hop and fast fall and l-cancel aerials, and then combine them. Any technique that doesn't require input from an opponent can and should be ground out in solo practice.
Tech chasing is a series of reactions you have to develop and be able to execute consistently and quickly. There are a lot of contingencies you have to prepare for, but the number is finite, and there are optimal ways to do it which cover the most options and give you the strongest punishes. Watch videos, take notes on how players like PPMD or M2K behave when they get a knockdown, and practice it mindfully when you get to play against human opponents. Maybe that means dthrowing more than usual in friendlies to get into that situation more often.
You'll need to be more specific about what help you need with punishing certain characters. In what position? At what percent? Are you close enough to get a grab or do you have to swing your sword to land a hit in time? It would take an essay to answer the question without any more information.
