I've never had tension rods fall out that quickly, although it is pretty common for them to detune and eventually fall out on Yamaha drums. Loc-Tite should work as Greg mentioned, but simply making sure the head is balanced and kept up to tension should help keep your rods from falling out. If the head isn't tuned evenly, the rods with less tension will vibrate loose. If the head doesn't have enough tension, all the rods will detune and loosen pretty fast.
On a related note: You'll probably find that the rods holding your Yamaha's "feet" will loosen a whole lot faster than the other ones. When I work with a Yamaha line, I usually remove the feet for this reason.
As for getting the snares to sit properly on the bottom head... I've noticed when installing Remo Marching Ambassadors on 13" Yamahas that the snare strands often can't make contact with the edges of the head because the rim gets in the way. With these collar-less heads, sometimes it takes a few days to stretch the head enough for the rim to clear the bearing edge. Get the head up to a medium-high tension, leave it for a day, tension it a bit more, leave it for another day, etc. If you go too fast, you could blow the bottom head. (In my case, they tend to blow right at the corner of the snare bed. That itty bitty little corner likes to cut right through the head, especially if the bearing edge isn't waxed.)