About gladiator show, you need 50 bucks in order to buy an amphyteatre, and then at least 20 to pay minimum class gladiators.
Note that sparing a fighter is many times better than killing him.
As for chariots.....you must have a very sensitive hand with the mouse, and try not to get in other chariots' way....maybe later I'll have more useful advice.
Btw, it seems the more country you've conquered. the easier you'll success in getting diplomatic alliances
A good way to make an alliance is to be diplomatic, than sound aggressive and finally offer alliance, asking for low, or in some cases normal tribute. This works most of the time.
