It's getting a bit late so I can't answer everything
1. What are some stuff I can lab with Corrin? I know IP and I'm just getting down B-reversals and wavebouncing (not to the point that I can use it naturally in a real match).
I just finally got time to start labbing and practicing myself, and here are some of the stuff I'm working on:
-walking (back and forth, after moves, after landing, etc, all while avoiding dashing)
-dash to shield (can be tricky to get the perfect timing since the game will buffer a roll if you press shield too soon)
-foxtrotting, dance-trotting/extended dashdancing, using moves directly after a foxtrot
-running and buffering moves after the skid animation
-pivot fsmash and pivot grab, the former being a bit tougher if you're using c-stick for attack
-perfect pivots (both empty perfect pivots and perfect pivot jab/dtilt)
-using jab/dtilt/IP out of shield
Some of these are really basic while others are more complex. Even simple stuff like dash to shield and moves OoS can be hard punished if messed up, so it's a good idea to be on point for everything. Some other stuff you can work on too are ledgetrumping, pinning the side of the stage, using fair's early autocancel to cancel DL landing lag and b-reverses/wavebounce which you already mentioned.
3. What are some of Corrin's strings that I can practice? I've got D-tilt to U-tilt or U-air and sometimes falling F-air to N or F-air.
Not an exhaustive list, but
this vid should cover most of the common stuff.
4. How can I improve Corrin's neutral game (kind of a more general question but I've been wanting to make it more solid)
I can't offer much help here since I'm also in the process of learning as a new competitive player, others can definitely give better insight. Basically, you're gonna want to stick in that zone Corrin controls with her superior range while staying outside the opponent's range. On this front, it's a good idea to be aware of your moves' range, how fast they come out, how laggy they are, etc. Patience is absolutely necessary; don't randomly throw out moves hoping they connect and at the same time, don't idly allow the enemy to invade your space. As Corrin, you will have to slowly and patiently creep in on the opponent, covering options with empty hops, spaced aerials and IP, to finally pressure them into a tough spot (either in the air for juggles or trapping them at the ledge). There are lot of posts in this thread where others describe Corrin's neutral much more in depth, but at the end of the day this is something you'll have to master through trial and error in actual matches.
5. Best way to practice spacing?
I don't know how training mode works on 3DS, but on Wii U this is what I started doing:
-Drop bombs around at 999%
-Hit them without getting hit yourself
-Fair/nair/bair practice (with bomb-ombs)
-Fair/bair practice (with goey bombs)
-Tipper Instant pin practice (with deku nuts)
-Pivot tipper down-angled fsmash practice (with deku nuts)
-Tipper fsmash practice (with hocotate bomb)
I can't guarantee this being the best way to practice spacing but I guess it's better than nothing.