1) Put simply: You're too early in the game to be worrying about synergy. Worry about Total Power, and know that you're going to be reliant on helper squads to clear harder maps (though this event is unusually easy in that regard, but story maps will kill your squads once you get into the upper tier (Missions 11 and Up).
2) Again, you don't have enough leveled units to begin worrying about synergy. It primarily comes into play once you're working with Teams made up almost entirely of 4* and above rarity units
3) Speed matters only on specific maps where you want one team to reach Point X before anyone reaches the flag, or to trigger switch nodes, etc. IIRC 11-3 is a good example of this. In general, you keep them roughly similar unless you have such maps or are trying to do speed-farming (clear maps ASAP without regard to 3*)
4) "Anti-pest squads" are squads with units like Toad Lily (halves damage taken from the tiny pests that fly around maps) and Edelweiss/Dianthus/Leucocoryne (heal on pest node). Missions 11 and up favor having at least one of these (especially 12-5 where you literally wade through about 15 pest nodes to reach the flag)
5) Level up. More specifically, if you want a speed-leveling strategy that's tried and true:
Step 1: Hit up the Friends list topics for some allies with strong helper squads
Step 2: Rush through the campaign maps relying on said helper squads to get you map clears (not complete aka 3*, just clear so you can progress to the next map)
Step 3: Reach 12-3, spam the hell out of it, putting all 5 squads on the top left camp so they skip the left and bottom sides of the map and go up around the top and down the right for quick runs to the flag. Your goal here is to get as many Secret Garden spawns as possible. Make sure you have ~115 stamina before running 12-3 so you're ready for if a SG spawns (costs 80 stamina).
Step 3b: If your stamina is too low, running 1-3 or 2-1 is an acceptable alternative if you need to use up some stamina (because you're going out or something) but your current stamina is too low for regular Step 3. This method only requires about 21-24 stamina but girl leveling is much slower
Notes: If you intend to use this method, level the hell out of a single girl (highest rarity you have) because your helper squad gets scaled down to the level of YOUR strongest girl.