Minor bathroom repairs - looking for advice

We need some minor bathroom work done in oru Eichler; however, I'm not
sure what type of contractor/handyman/... would do this work.
Recommendations are welcome.

1) We recently had our bathroom floor replaced - the old floor was
Pergo, and the new floor is tile. The Pergo floor was about a 1/2
inch thicker than the tile floor, so now there is about a 1/2 inch gap
between the tile floor and the wooden door uprights (or whatever you
call the trim around a door). I'm guessing this gap needs to filled
in with (fill in the blank) before it's painted over?

2) Second, the tile design was done on a diagonal, so the edge, near
the entrance is somewhat jagged. Our hallway floor is also Pergo, and
we had a Pergo transition strip/lip placed between the hallway and
bathroom floor, to cover up this jagged edge. This mostly
worked... however, once the gaps, described in (1), are filled in,
there will be a small (about 1 square millimeter) gap/hole between the
end of the tile and the Pergo transition strip. I'm hoping this small
hole can be filled in with come kind of hard compound that closely
matches the color of the tile (off-white). We're talking about a
really small hole, so as long as the color/brightness of the tile and
compound are close, I think that would be good enough. What would be
the best way fix this small hole?

Once this work is done, we plan on repainting the entire bathroom. Is
this the type of fixup work a painter should be able to do? Or is it
better to get someone else to do this minor work before hiring a
painter?

Thanks for any advice
[email protected]
Palo Alto