From my limited knowledge injuries don't get healed. Guido can shed more light on this.
I don't think there is anything extra a new manager should know.
Earlier in the old market after the new season started we only had only Nordeus generated ( super fast trainers ) players in the market. Instead of the few players we see in the market at one time we had a lot of players and every server had their own market. The market refresh time was about 3 hours approx instead of 4 min.
So if you had money you could build a squad of fast trainers in hours. Managers with unfavourable time zones used to be awake to recruit these players. These were the golden old days when everyone eagerly waited for new season to start.