In our group you can buy talents and stats at any time, skills advancements if you used the skill and new skills between mission if you have enough time and a teacher. (depends on the skill, I would allow learning dodge from another character in an evening or two, but not a whole new language or tech-use.

Can train any time between sessions, or during downtime mid session at my table. Only thing that couldn't be trained between sessions (without first having downtime) would be psychic powers.

I allow anything to be trained / learned between sessions and very rarely during sessions (the only time this has occured was when the Tech-Priest jumped out of the 2nd floor of a burning mansion holding a slightly insane old noble woman and he asked, after he jumped that is, if he could buy that levitation ability that tech-priests can get).