Answers you receive will probably vary ...
1. For their size, should I put them in larger pots?
Yes, sarrs will develop an extensive root system if you give them room.
They should be fine in thier current pots for a season or two though.
2. Do they need the water trays I have them in?
Yes. Some will say water when tray goes dry. But I usually always keep water in mine. About an inch or so. I think some in the warmer states have had issues with bacteria when doing this. Soil should be damp to touch but water should not gather in the impression you have made with your finger in the soil. At least that is the rule of thumb I have read and used.
3. Since we're still up in the air about the beetles, should I move the table back into the full sunlight (by the raspberry bushes in the background)??
Yes, sarrs need at least 8 hours of sun for best results. I try to give mine 10-12 when possible.
Tips, tricks, etc.
Trim off dead or dying pitchers that have become overfilled with bugs to prevent rotting.
Your biggest challenge will probably be dormancy. I suggest you do some research and find what suits you best. Psittacina and leucophylla are less cold resistant in my experience and/or reading.