1) I'm not sure how custom collision masks per-tile would fit in to the editor. How workable would it be just to place sprites on top and use them for collisions as well? It seems to be a good middle ground.
2) It's far more efficient like that - it's more like using a series of tiled backgrounds in the most optimal way possible. I'll cover how this works in a technical blog soon.
3) Only if it's essential - is it really badly needed?
4-5) The current tilemap editor is very much a first iteration. We'll be improving it over time.
inkBot:
You can't move the tilemap if you have any tool other than the select tool chosen. You can also stamp sets of tiles by selecting a larger area of tiles with the pencil tool.
With regards to advanced features, for now we're taking a similar stance as the image editor: we get tonnes of feature requests, and we're a small team, so we want to get everything covered as well as possible. That means not getting stuck down rabbit holes making the image editor as good as Photoshop when Photoshop already exists, and I think the same thing with the tilemap editor with regards to Tiled. It's a lot of work to reinvent the wheel when the importer seems to work just fine, and the built-in editor serves well for tweaks or small-scale design.