Flew to/from there many times, but haven't connected internationally in the last 10 years.

Itinerary is OAK-LAX-LHR r/t domestic segments on SkyWest, TATL on VS.
I have 3 hr layover on each way.

Am I correct that my domestic flight departs/arrives at T3, while VS does it at T2 ?
Is there an easy passage within security from T3 to T2 on the way out ?
What is the latest on the SC refurbishment at T3 ? Last April we were given ramen in styrofoam and it was supercrowded. Any chance I could use the VS lounge also coming back, JFK-style ?

TIA