For the first case, you need to have a single texture in that case. If the texture is too large, then there are other tricks that I know of, rather simple ones, that allow for getting rid of the seam, but it would take modifications of your textures and it may not work (I haven't tested it yet).

For the second case, you can resize blocks to use a larger texture. Either that, or use a model instead as model-only levels have tons of major advantages than levels made from blocks.

For the third case, what I'm referring to is using the ent_create command in your script. If you ent_create entities that use this position where the gap is, odd things can happen.

What edition do you have? 6.20.2 is an old version. I suggest updating it to the latest version, 6.40.5. It's a free update. Although this will unlikely fix the tiling issue, it can help to some extent.