Hard for me to do it any other way but equatorial. The answers to your questions are "it depends." I fully remove counterweight shaft and counterweights because I do 98% of my observing at a remote site. Keeping everything assembled is very difficult and makes for an awkward mass. Not mess, I mean MASS. Counterweights and a mount and all that can be a bit much to handle and they move in unpredictable ways. Plus it's all heavy! Break it down and it's easier to handle.
If you have it assembled such that you can just lift the whole thing and take it out the door, then you would leave it all assembled. This would be extremely awkward to do with a 10 kilo OTA which I think is what you have, in such a way that you don't bang stuff up. The most I would want to move is tripod + GEM head with the counterweights off and the scope off. The counterweight shaft is a definite "maybe" in such short distance transport, maybe on, maybe off.
Weight position: I have so many different rigs that usually I just test the balance. If you have one rig you can mark, or get to know by sight and habit, the correct placement of the counterweights. In DEC on the other hand you've got two things going on. 1. You can move the telescope on its dovetail within the saddle for balance. 2. You can move the tube *within the rings* for balance. Make sure you know EXACTLY what you are doing in both cases, if you loosen the rings to move the refractor then tighten them up again, and if you loosen the saddle make sure you tighten that up again. The Dec balance has to be done with the scope as you would use it: Diagonal in, finder on, dust cover off, and one of your larger eyepieces. Now when you've got it all balanced it is convenient to have a mark to find that spot again. I put a scratch on my dovetail because I'm uninhibited about that sort of thing and as I say, some of this stuff I'll be dead before I sell it.
If you get the thing reasonably lined up on true N, you will have an immense advantage in looking for stuff: the directions in which your telescope moves are EXACTLY the same as the lines you see on star charts. You're not as reliant on pattern hopping as in alt-az. If it's a *good* German equatorial it will be very solid in the wind and allow for very precise control of the telescope for purposes of centering and looking around, assuming you have tracking.
I keep my tripods wrapped in moving blankets for cosmetic protection and over twenty years I've grown less concerned about the G11. It can take care of itself. I don't mean less concerned in the sense that I want it to stop working. I mean I have a high degree of confidence in its ability to handle being casually handled. I'm probably going to have it until I'm dead but even if I don't it's one of the least expensive things I've owned, figure it out, $2,000 to purchase works out to $100 a year.
Other kinds of mounts are more vulnerable such as AVX the outer casing is not as tough as a G11. Kinda egg-shell-y by comparison.
HINT: On polar alignment, leveling the mount will make it easier the NEXT time you set up. That is, with a new mount you have to get the altitude correct for your latitude. Once you find that spot, it's good for as long as you live at that latitude. By leveling, you go back to the correct declination automatically after that. Which means that the main "centering" task will be the left-right (azimuth) adjustment to get the scope pointed due north. If you're interested in precise alignment you'll have to fine tune, typically with a polar scope (or computerized suggestions).
But you don't need to level, it's just convenient for the next time you set up.
If you're using a go-to system try to nail a star on the east side of the mount first. Most systems seem happiest with that.
This is a ten kilo tube. I hope you have a good mount. If you find you got the shakes "consider the G11."