...Do all POS/POS+POW wallet cryptocurrencies need to be running 24 hours per day in order to mint?

Sort of. You are only forging when your client is running and forging is turned on. However, forging in Qora isn't a time-based system where your account is placed in a form of "queue" where larger balances get higher priority and when it's your turn, you get to forge a block if your client is available.

Instead, the larger your balance the better the chances of you finding a block.

Regarding the forging algorithm, every 10 blocks Qora recalculates it's difficulty. In a nutshell, it looks at how long it took to mine those previous 10 blocks, looks at the total number of coins held by each forger and then derives a new difficulty. 10 blocks should take ~10 minutes to forge. If it takes more or less than 10 minutes then difficulty will be scaled based off of the time and the balances that were used to forged the previous 10 blocks.

If I recall correctly, time might also be a factor of difficulty when forging a specific block. In other words, the longer it takes to forge a block, relative difficulty my decrease so that smaller accounts can find a block.

Personally, I think the algo could be tweaked such that if a few MAJOR wallets go offline then the, smaller accounts can quickly forge and re-adjust to a relative difficulty. Also, I think the difficulty adjustment period could be lowered (to possibly every block but certainly every 2-3 blocks) and then recalculated based off of the previous 10-20 blocks using more specific mathematics than simple averages.

I've not written any form of spec about it coz I've not thought about it enough to present any details that could make the block-process function more smoothly with time. Also, I need to be sure I fully understand the Qora algorithm. At the momement, I think I've wrapped my head around about 85% of the process.