For things like farming toyko exploration, having a pocket techter for buffs/zanverse/heals, extra account rewards to sell on the market, etc. Is this allowed to have 2+ clients running at the same time, and does the game even allow two instances of the client? (Note: I would never do this in multi-player content)

You can't run the same instance of a client because of game guard. (IE: using the same files, but opening it again.) You'd have to dual-box instead. This is something that some people do even in pay to plays, and is not exactly against the rules, since it's two different accounts, with two different data sets.

Otherwise they'd have to not allow, let's say your significant other... to help you do the same thing, on another computer or console.

The general rule of thumb is it's fine, so long as you're not using a third party software to actively control both characters and utilize inputs on both clients at the exact same time.