Team wars is probably the one event where you and the team will be able to shine.
Here are probably all the solutions to get you easy point during a race.
When asked to breed commons: You want to do firesaur + greenasaur.
When asked to breed uncommons: You want to do pandaken + one of the two above.
When asked to breed rares: You want pandaken + one of the two above.
When asked to breed epics: You want to do rabidex + fliploch (or other combination).
When the numbers asked are big, do them all if you can, this is how you maximise points.
Epics are always 1d8H to breed (unless you activate shrines)
If you have both the breeding moutain and forest start an epic in one of them and wait to hatch it when it is required and it saves your other breeding terrain for easier breeds.
You can use gems as pleased. I never buy gems, I save the free ones between races and I can use them to buy tougher quest. I usually enter a race with 300 gems that were given in the game so I invest 0 real dollars.
Food and gold pickup event are usually the events where the team is required to participate the most. Stay clear of events where one member must do it, let the high level players get those out of the way, but the events where 15 members are expected to do it, you need to chip in.