I can’t answer your first question as I’m revisiting the game from a long while back and they’ve apparently changed how loyalty works. I think there are now events you need to spend EP’s on to affect loyalty for the British in the revolution scenario. As far as I can tell the old method of spamming loyalty reductions/increases across the map every time a strategic town switched sides is gone.
On the British strategy, what is more efficient, running after the American everywhere trying (vainly) to engage them in battle? Or should you just slowly take control of territory trying to garrison structures but insuring you don't lose many garrison to assault?
Trying to kill Continentals is like playing whack-a-mole, but the game never ends and you’ll be chasing moles all over the place until the very last turn. Your best bet is to secure all/most coastal objectives first, then use the larger cities like New York and Philadelphia as supply bases to launch campaigns into the interior.
I keep a decent sized force at my main supply base, and then leave one or two units in cleared out regions along a route towards my current campaign objective (this allows swift movement of supply units to and from the front line). Once the objective is secure, I retract my lines and reform for the next campaign.
A good example as to why you need to focus around large supply bases is what happened in my current game. I tried hanging on to Boston from the very start, but supply production was simply inadequate which forced me to pull out more than half my starting troops. The remaining small force was then pounded for several months in a row by the Continentals and I was eventually forced to leave altogether due to the inability to rebuild my damaged elements.
A good option for the Boston troops is to shuttle about half of them into Norfolk, supply production is good enough there to support a large force and it’s a good place to launch a short campaign into Virginia from.
Finally I’ve learned not to leave my British garrisons inside of towns unless they are Tory units. Unlike the continentals, you can’t rebuild lost combat units, so never leave British or German units in a situation where they may get completely destroyed. Better to fight outside of town and retreat than to die inside. Only your Tory units get rebuilt when lost, so those you can risk losing.