You can store as much in one bag as you want really - don't forget, 35mm will be in canisters and 120 will be in their own foiled/sealed wrappers anyway (in addition to cardboard box packaging) so they will have multiple layers to protect them anyway.
As for the processing, some people do, but depends on the time between exposure and processing really. If you know it's going to be a long time then it is the general advice to keep it stored in a cool place till processing - same rules apply, ensure it is properly bagged up and allowed to come back up to room temperature.
But for many films, don't worry. I only mention Velvia because it tends to have a "pro film" storage requirement to it - most general consumer film on the other hand is often designed for absolute stability even in poor storage conditions, something they are more likely to be subjected to in the hands of a consumer/amateur (which sounds like a horrible thing to say, but I hope you get what I am trying to describe).