YEs this is good. since you can use the logi to power the PSU,s thats a good way to go. or just set the PSUs to always-on via the logic, and switch the mains, which is what I do.
always a good move. usually, when going to charge something, I set to a voltage close to the battery (50V) and have the current limited to like 1A, then connect the output/
yes totally fine. if there is no output there is no current, but the voltage will go up. To be safe you can use a dmm and measure the output of the converter and see if its over-spec or something. like set to 50.4v and measure. anything within a few thents of a volt is fine. the actual battery will only be charged to the cutoff of the BMS.
Remember that if you power on with a battery as a source , you dont have the current protection of the PSUs. unless you’re in a rush, i would build the PSU stack first. and test with that