1- pretty sure it doesn't matter. i think the only method in the game for increasing research time is the tier 1 civilian tech that the Advent has.
2- if the Marza is part of a fleet, make sure you don't give the fleet any orders that would override the missile barrage. sometimes the fleet AI will interpret orders given to the lead ship of the fleet as orders given to the whole fleet. its inconsistent in this regard, doens't always happen but sometimes it does. something to watch out for, in addition to the other things you've tried.
3- whenever i've got a fleet of 4+ cap ships in it by default i keep all autocasts turned off. when a battle starts ill look at what i'm up against and then switch on the autocasts i want to use. its much easier this way than to try to micro the abilities of 5 different caps, i don't trust myself enough to get peak efficiency with that much going on at once.
regarding hotkeys, i generally just hotkey the fleet itself and use tab and shift+tab to run through the cap ships in the fleet. its pretty fast that way and doesn't require me to remember a half dozen or more different control groups.
4- have to take all his worlds. the planet designated "homeworld" can be moved actually, its a planet infrastructure upgrade. your starting world has it built by default but you can build it somewhere else (one per empire) if you want to or need to.