Can I command a conjured animal to do multiple things, and at any time? Can I change my command any time or on my next turn?
The spell Conjure animals gives you a pretty good idea of what you can do concerning animals that are conjured by the spell.
You summon creatures, and can issue verbal commands to them. They attempt to follow the commands as well as they can, and any new command you give them supersedes any prior commands.
If you summon more beasts of a lower CR (rats for example), you can issue them each individual commands and they will obey to the best of their ability. As is normal, Any new commands given will supersede old commands.
Issuing a command doesn't require any actions(as specified by the spell), but animals will likely not remember commands you give them beyond the first.(Animals aren't normally intelligent enough to do so)
However, the things that you could do with this spell should be ran by your GM, as he may have a different opinion.