Cloaking's effects on your ship are listed as giving the ability to hack, and affecting how high the success chances of your hack will be.

The CipherBot's effect gives "+7% Hacking".

Scanning's effects on your ship includes "[Increased] hacking potential" among its effects.

So this is my question: How do they stack, and how do they work?

Cloaking's effects are rather obvious, but does the CipherBot's effect give you a 7% high chance of success in a hack, 7% more research, or both? Does scanning's increased hacking potential mean that you will average more research stolen per hack? If so, how much? Is it worth it?

Thanks.

the +% hacking and +% raiding modules increase the chance of a hack or raid, not the amount hacked or raided

when you are hacking....

first your cloak (including all buffs and debuffs that directly affect cloak only) is compared against the opposing ship's scan (including all buffs and debuffs that directly affect scan only)
this determines whether or not you will even be able to attempt a hack... if your cloak is higher, you have a hack button you can press

second, your cloak (including cloak buffs and debuffs) + your scan (including scan buffs and debuffs) is compared against the opposing ship's cloak (including cloak buffs and debuffs) + scan (including scan buffs and debuffs) in an equation pretty much hidden from us to determine chance of success in hacking... it is this chance of success that is multiplied by 1.07ⁿ where n = # of cipherbots you have

I see, so none of it affects amount hacked, and since having a lone CipherBot on my ship allows me to hack nearly everyone my rank (successfully probably 97% of the time), equipping scanners will not provide me any noticeable bonus?

it might increase your chance at critical hacks

RigorMortis, "MIGHT" is the operative word. This is one of the few calculations/equations that hasn't been fully cracked yet.