Hi Michael,
Welcome and congratulations on your purchase.
Jonathan has just replied but here's my version.
Q1: We all sail downwind with not a great amount of contribution from the jib, unless dead downwind and with it poled out to the opposite side from the mainsail, so no problems there. In strong winds from astern, some have concerns about the mizzen forcing a broach but I haven't found this to be a problem so far. Upwind, you'll find that weather helm is increased without the jib but as you've probably already found, it should be manageable. Don't worry too much about shroud tension, as long as the mast isn't waggling about, isn't leaning to leeward much in the tabernacle and the windward shroud is taut. One way of increasing shroud tension without flying the jib is to use the spinnaker halyard (if you have one) to raise the back of the jib boom up a bit. That's what Jonathan calls his topping lift, essential on a BRe. This is also a good way of playing with jib leech tension in light airs. Assuming that your BR is gunter-rigged, you may need a halyard crane on top of the mast to separate the forestay from the jib furler. Alternatively, a fiddle block (original equipment on some BR's with spinnakers) may provide a bit of separation between the two lines. In strong winds, I leave my bowsprit (mostly used for my second foresail, a flying jib) in the car and am happy to do without any sort of forestay. As for the jib furling line, make sure that it goes into the furler square on and dead centre and keep some tension on the outhaul as you furl it in. When you let the jib out, make sure that you cleat off the furler line with a small amount of tension in it once you have fully unfurled. Don't have too much line left on the drum when the jib is furled. My furler was always jamming until I figured this out.
Q2: Yes, if the mizzen is sheeted in amidships (and that is how you want it to stay), then like the self-tacking jib, it can be left to its own devices when tacking. As for jibing the mainsail, I grab the mainsheet as it swings across to stop it crashing on the other side. Or if I want it to jibe without changing course or wind angle, I grab the mainsheet and pull it over, until it reaches the angle when it will jibe. I then hang on as long as I can to cushion the jibe. Others (including Jonathan) have more sophisticated techniques!
Q3: I used to have problems with the yard sticking up and down the mast because my gunter jaws were set too narrow. I forced them apart a bit and it solved the problem. Make sure that the parrel bead strops around the front of the mast are not too tight. I always make sure that all lines down the mast are outside of all the parrel bead strops and never have any problems with the yard snagging on anything. When I let go the main halyard (as long as the mainsheet is off and I'm more or less facing into the wind) the whole lot comes crashing down into a neat pile on top of the sprit boom, guided down and held in place by my double topping lift.
Solving niggles is half the fun! And you can learn all sorts of tricks from sailing in company with other BR's and BRe's at one of the rallies or raids. Perhaps not so easy from Belfast.