After a tile is placed but before a player indicates the turn is over by saying "Done", may he move a tile from his rack to a different position on the table after he has initially placed it? May he place a tile down and then decide to remove it or replace it before saying "done"? Or once it is on the table in a certain position it must stay there?
During your turn, you can pretty much do whatever you see fit with every tile on the table, including those you've only just placed. As long as the end result has no invalid sets. Except, apparently, joker tiles:
With the exception of the joker, any tile on the table may be repositioned provided that all tiles on the board eventually become part of a meld. The joker may be used in place of any tile when forming melds, but once a joker is on the table it cannot be moved to another meld. It must first be replaced by the tile for which it was used.
I cite this source, because it seems to be the most reliable one. But, truthfully, I wasn't aware of the joker exception.
There are many variations on the rummikub rules (see this link) which makes it difficult to give a quote to answer your question(s). So I'll answer based on the rules which were in the version I used to play.
- All tiles on the table may be moved about by the person whose go it is, with the exception of any set/run which has a joker in it.
- The player may add tiles from his hand to the table at any point during his go.
- If, at the end of his go, the player cannot move all tiles into valid sets/runs of at least 3, he must pick up any leftover tiles plus a penalty of three tiles from the draw stack.
So, after rearranging tiles on the table, yes a player is allowed to add tiles from his hand. He may add tiles from his hand, and then rearrange tiles (including the tile he placed) as much as he likes (as long as he doesn't break up a set/run with a joker in it). But he cannot place a tile from his hand and then pick it back up, unless he takes the 3 tile penalty.