Yes, you should be fine. Processing times are around three weeks. So you have plenty of time.
Upload all of your documents on the TLSConnect site. You will just need to print out the checklist and take that with you to your appointment.
There they will take your prints, photos and passport.
No need to submit flights or hotel details. They’ve specifically said they don’t want that info.
No need to prove medical cover.
TB test only needed if you’re going for more than six months. In that case a visitor visa is not suitable, anyway.
I have applied 4 times and currently waiting on my 5th visa. Should be ready next week.
My wife has applied for a two year visa about a week ago and there was no need for a TB test.