At least this is a great learning project! I finished almost none of my projects (continuity *cough*) but I learned a lot from doing all things. Hope you can get something nice out this though.

looking nice so far, that is nice and smooth movement

Here are a couple tips I could think of

Instead of sticking your tilemap drawing code inside the main loop (since you're not gonna be changing any tiles), you can stick it outside of the loop and StorePic to L3 (assuming you're willing to sacrifice that) and every loop through the main loop, just use RecallPic.

Also, for your collision routines, it's much easier to have a routine called GetT or something that returns the tile that a certain point is in. For instance, with your 8x8 tiles, you'd use:

Lbl GetT
Return {r2/8*12+(r1/8)+GDB0}

And since you're just checking for the empty ones, write another routine

Lbl CheckE
Return GetT(r1,r2)<1

or whatever. I've left it unoptimized for clarity - sometimes, this isn't the best way to do it, but it's good for many cases. That way you can rewrite

X-(getKey(2) and CheckE(X-1,Y) and CheckE(X-1,Y+7)) + (getKey(3) and CheckE(X+8,Y) and CheckE(X+8,Y+7))→X

Of course, there are much better ways to check for collisions, but I'll leave that as an exercise for you

Instead of sticking your tilemap drawing code inside the main loop (since you're not gonna be changing any tiles), you can stick it outside of the loop and StorePic to L3 (assuming you're willing to sacrifice that) and every loop through the main loop, just use RecallPic.

Can this also be done with greyscale?

No; With greyscale, you'll likely have to add additional buffers or use L1. Of course, if you have a simple character like yours, you can just AND it off the frame before drawing it again the next frame, and then you won't have to redraw any part of the tilemap.

So what you can try doing is something like

Main loop
Your code
Pt-On(X,Y,Picwhatever)
DispGraph
Pt-Change(X,Y,Picwhatever)
End loop

That'll make sure your character is erased before the next frame, so you don't have to use RecallPic anymore.

You need to use free RAM and not program variables. (i.e. use the bytes in L1 and don't store new values to your original map, say GDB0 or whatever)