To specifically answer your questions:
1. Can I store different kinds of rice in the same container?
Sorry, at first I thought you meant to mix different types of rice together in the same container. Still, I would recommend against this option, unless you are using smaller plastic or glass container with tight-fitting lids to separate the rice, then putting those containers in your larger container. I would not put rice in the kind of plastic or paper bags you get at the grocer or buy online, and then store them in the larger container. Those bags are meant to be sold immediately, or within a shorter period of time than you want to store the rice. I would think that it would invite moisture and/or mold into the container. Don't overcrowd the larger container -- the lid has to have room to go on and remain tight-fitting for the duration.
2: how many of those packets per container?
I would not use them, especially if you are considering placing them in the container with the rice. Most of them are not food-grade and can degrade.
Here's some info on silica gel packs. . Just make sure you're buying food-grade packs regardless of the active ingredients if you're going to use them.
I worked in a Japanese restaurant for 8 years (on the east end of Long Island -- where it's hot and damp for about half the year). We regularly bought, unpacked and stored 3 types of rice in 5 or 6 30-gallon food grade containers stored in the not climate controlled basement of a 100-year old building. We did not use the packets you are referring to at all, although we did go through that rice in about 4 months.
Take a hard look at where you're seeing those packets in food storage. Chances are, you're seeing them in commercially prepared and refrigerated foods -- i.e. in environments where it's cool and damp-- like a refrigerator. It's been my experience that those little packets draw moisture to them, but they don't necessarily keep the moisture away from the food they are touching. Consider using them in the storage room where you'll keep the rice, or in the larger container where you're storing rice in smaller individual containers, but not directly on or touching the rice. Ask about the capacity to wick moisture from the air from the mfg of the desiccant as they vary from size and active ingredient.
3 does the container have to be filled to the top?
No, I don't think so. It's probably more important that the container is clean, dry and in good shape and that the lid fits snugly. By that I mean that small critters -- ants and other bugs won't be able to find a break in the seal, and the rats won't be able to lift the lid, or chew through the container.
Regardless, inspect the containers at least every 6 months or even every 3 months if they are in long-term storage. Check for loose fitting lids (does the lid jiggle when you shake it?) and move the containers out of the storage area to inspect the back and bottoms of them for ah, chewing animals.