Brand new here - questions about Phal care

[Fuzzy]

Dear Forum,

I'm a brand new orchid owner. I got my first Phal (the full name is Phal. Baldan's Kaleidoscope 'Golden Treasure' AM/AOS) two weeks ago. It is now in full bloom and has about 15 gorgeous flowers. It's quite a big plant. The leaves are about 8" long and the stem is over 2 feet long. I'm in love with this orchid, and want to do my best to give it a good and happy life. So here are my questions.

1. It came in this very thin and flimsy 6" plastic pot and the roots are showing. A couple are even hanging out. Is this pot too small and does it need repotting? Just to give you an idea, the pot is so small and light that the orchid would topple over if held in this pot. I have put the small pot into a bigger planter (filled with some paper towels to prop it up). Is this fine or do I need to repot?

2. I've had the plant for 2 weeks and it looks great and seems to be thriving. It's getting a few hours of indirect sunlight and some direct light daily (south exposure). I water it weekly by adding about 4 cups of water and waiting for it to drain fully. It takes up about 1/2 cup to a cup at each watering. Does this regimen sound about right? Should I keep doing what I'm doing?

3. Fertilizer. The big question is, do I need to fertilize? I've found some articles that say you must. If so, should I buy the 20-20-20 orchid fertiliser, or go with the one to encourage re-blooming? I would love to have it re-bloom, naturally.

I think this is all for now. Thanks for bearing with me!!

-Fuzzy