Now, for moving here is what I suggest. Practice various technical movement options. Learn foxtrot/Foxtrot dancing, Dash-Shield, Phasing and other easy stuff. You probably already know these, but here is what I do. I use all these things in TM. I just Foxtrot around, mixing it up with Phase Uairs/fairs and all those other simple movement options. This will help you get used to simply using them whenever you need to. Also, practice U-turn and walking, as U-turn can be useful and walking is a GDLK ability. Eventually, once you learn stuff like PP and LC, implement those into your practice. It shouldn't take more then a couple of weeks to become proficient with the easier movement options.
For the second part, there is a gigantic mistake I often see even in the best players. They use confusion with FH distance of the ground. This enables the opponent to easily punish you without over-committing. Using it higher up will force the opponent to land it they want to combo you. Chances are that whatever single aerial they can get out of a DJ isn't going to harm you that much. Also, teleporting into the stage can be a really good mix-up option. Better then one would think as the opponent is going to approach the spot where they believe you will land.
