I'm getting back into cubing after a long absence and trying to recover back to where I was 2 years ago and then start moving forward again...
I've re-learned how to solve my 3x3 using Roux. I have never learned CFOP. At one point I knew the beginner's method but have not used it for a long time.
My next step (along with improving my Roux) is to re-learn how to solve my 4x4 and then to generalize up to 5x5, 6x6, etc...
The method I have in my notes from 2 years ago is a reduction based method, but what I've found out is that most of my notes were based on my level of knowledge at that time and I don't always understand what I wrote then

Here's what I have...
1 Solve centers (create center pairs and join them)
2 Pair dedges
Place dedges across from each other, pair them, shuffle them to another side, then repair the center damage
3 To solve the last two dedges on the front L/R:
Dd R F' U R' F Dd' (Dd means BOTH layers, like a wide turn on a 3x3)
4 Solve using any 3x3 method
5 Final parity fixes: (need to unify notations)
Front/top dedge flipped:
z d' m D l' u' 2R' u l u' l2' b' 2R' b r' R' 2U y' m' u x2 z'
Top front/back dedges swapped: (lowercase is inner layer) GOOD!
Uu2 Rr2 U2 r2 U2 Rr2 Uu2
Right now I can solve the centers fine. Pairing the dedges is coming back to me, I'm able to do it but I lack the more explicit notes I once had about exactly where to put other bad dedges to prevent breaking them. I should be able to get that nailed down fairly soon. Once it's reduced to 3x3, I solve it using Roux, then apply a parity fix if necessary. As noted, I need to unify my parity algorithm notations. Currently I was just able to solve my 4x4 but I have to follow the parity algorithms slowly by hand until I relearn them and the dedges are clumsy too.
Note that I'm more concerned with easier learning/less algorithms than being super-fast, this is just for solving and not for competition.
That's all just background. Here are the questions...
1. I'd like to eventually do 5x5, 6x6, and maybe even 7x7 but I do not expect to go higher. Should I learn a better method that will scale from 4x4 to 7x7? What would that be? I'm kind of looking at Meyer as a possibility but not sure the relative advantages of this compared to reduction.
2. Do odd cube sizes still have parity? I've heard that if you learn 4x4 and 5x5 that basically gives you the ability to solve any size, is that right?
3. Given that I only know Roux, how screwed am I once sizes are big enough that I can't do M slices anymore? At what size will that happen?
Thanks!