Hey there Anni! Welcome to the fold!!
Frost on the scope is not a worry. In fact, it's a given on these cold days of winter, at least for those of us in the North! I personally keep my ep's in a case, with the lid down, to keep them from frosting over. If you do manage to get frost on one though, simply stick it in your pocket for a bit (be sure there's nothing else in your pocket that could scratch the lenses though).
Once you're ready to come inside, you have 2 choices. 1) lock everything into air-tight containers, so that no moisture will settle on them as they warm up, or 2) leave everything out in the open. They'll get wet as the indoor humidity condenses on the cold metal/glass, but it'll soon evaporate as the scope comes back up to room temp. Once it is at room temp, it's safe to stow away or cover. Water droplets on your primary mirror should just be ignored. They have no impact on your viewing. Cleaning should be kept to an absolute minimum. EP's, on the other hand, can be easily cleaned using a mixture of 90% (or higher) isopropal alcohol and distilled water and a Q-tip. Very lighting brush away any dirt with a soft, camel hair brush, then dip your Q-tip in the mixture and very lighty swipe the lens. Should do the trick!
Can't really answer the eq. mount questions, as I use an alt/az mount.
There's 90 degree finder scopes out there for your neck breaking problem at zenith.
Hope this helped a little! Wally