I sat down with an emulator to test some things out.

TL;DR for speed you want to: hold right always jump for 1 frame release as quickly as possible on the frame you land you need to hold jump but just holding it while you land is fine. (for a 1 frame jump the frame you land will be the 21st frame) 5 frames after you land you're allowed to jump again and you can repeat 1 frame jumps like this

Another tidbit is that you can cancel your bark animation on the 2nd (or 3rd?) frame after landing with a crouch and then do a new jump on the 5th frame after landing and continue to jump without loosing any speed.

Here's a graph of your current speed in subpixels (sp) against the time (f) in frames: http://imgur.com/xs0ihkB

From what I can gather the halfword in $C80 in the WRAM is your pixel speed on that frame and the halfword in $C27 is your subpixel speed. In the graph these two are added together assuming a pixel has 256 subdivisions and then plotted against the frame count during jumps.

To gather the distance traveled you need to calculate the area that the trapezoid covers but I have not bothered to do that since I feel it's obvious that the red covers a larger area than the blue although the difference isn't huge. The difference is much larger when you compare them from standstill: http://imgur.com/fgKvoSS . In this graph you can also see that whenever you're falling you're accelerating towards your aerial horizontal max speed (~$400-$410 or $200 or 500 sp/f). If you exceed it you'll decelerate at the same pace. Jumping usually gives a large speed boost unless you're close to certain objects which will reset your speed to 0 if you jump. Also if you fail to hold jump when landing your speed will lower significantly.

Some other interesting addresses found: $177E - X position? $17D8 - Y position $17DE - first enemy slot Y position? $1F5C - Seem to work as a timer for a gravity switch when jumping $1628 - HP $15C6 - Lives $1F92 - Bark Charge (starts at 0, +1 for every frame held, infinite?) $162A - Timer for water powerup until evaporation (720 f) $1654 - Timer count $1656 - Frames until next decrease of Timer (180 f) $15B6 - Current level in order, $7 triggers credits, higher values crashes game after some nice glitchyness. If you can find a way to alter this value you could wrong warp between levels and to the credits ;).

Here's a quick TAS of the first level:

That's all for now.