Hello and welcome!
Your research is correct. You have a phalaenopsis orchid. You should trim the two spikes about one inch above where they grow out of the plant. This will force the plant to put energy into the leaves and roots. This plant will bloom again for you next season. The roots look very healthy. You can follow my video guide to repotting your phal here:
As for the pot, if you place it inside another 'decorative' pot, please make sure the orchid roots get plenty of air and water drains freely. See this article for lots of helpful information on phal orchids.
https://www.rv-orchidworks.com/orchi...-(Moth-Orchid)
Also, lots of good info here too:
https://www.rv-orchidworks.com/orchi...nopsis-orchids
Cheers,
BD