If all 3 of us apply together, will the application be processed together? Is it a better idea for me to apply separately to make sure the wife and/or kid get approval faster if their applications are more straightforward or processed in parallel?
Each applicant is processed individually. It makes no difference how you apply. THey are not processed together as a family application whether you apply together or not.
Can I choose a different Council for the Oath ceremony and do some research to see which is the fastest or HO always sends the letter to the local council?
You can but you could end up disappointed. What might be quicker now, is possible to be delayed in a few months. Not many councils are currently severely delayed.
What time are the free appointments released on UKVCAS? 12AM or 9AM? Are there free appointments on weekends?
Like asking how long is a piece of string. It is hugely dependent on your area and how flexible you are. Free appointments however are few and get snapped up really quickly.
