The only way to continue moving while switching weapons, is via a client side mod. I don't know if this is on the approved list or not, but Arma as of yet, to my knowledge, has not allowed for weapon swapping on the move.
The issue you're having with weapon toggle (up and down) has to do with AGM. Load yourself into the editor, his your ESC key, and you'll see up in the top left corner of your screen, AGM Settings. Top of my head, I can't remember what two (2) settings use CTRL (which is overriding your Arma keybind). One has something to do with showing names, I think. It's on the front page. Disable them, and your keybinds will return.
I haven't had any issues with stances or grenades. For your grenades, are you using the vanilla Arma keybinds? AGM allows you to cycle through them using the 6 and 7 keys. 6 cycles through lethal grenades, and 7 through non-lethal. CTRL+G cycles through the grenade throw options, and then finally G throw says grenade.
I don't think Podagork has any preview map thing. As long as it loads up without errors, I'd say it's working as intended.