In comparisons, you can use 'से ज़्यादा' - more than'. Outside of comparisons, ज़्यादा works like 'a lot'/'much'/'many'.
Eg: मैं चार घंटों से ज़्यादा हवाई जहाज़ में बैठ नहीं सकता। इसलिए मैं ज़्यादा सफ़र नहीं करता। (I can't sit in an airplane for more than 4 hours. So I don't travel a lot.')
और is not used in comparisons. It just means 'more' or 'more than currently'. Eg: उसे और पैसे दो - Give him some more money
Yes, पैसे is the subject of the hindi sentence.
It's confusing because the english translation somehow has a different subject ("she"). How can the subject switch? Because the verb switched! In english the verb is "has" but hindi has no verb "to have". We like to pretend that के पास can be translated as "has" but के पास is not actually a verb. The verb in the hindi sentence is होना ("to be") which is what you are trying to conjugate as either है or हैं. If we tried to make an english translation using the verb "to be" we would come up with something like "there is more money in her possesion than in yours". Nobody talks like that in english, but the point is you can see that the subject is clearly "money" if "has" didnt exist and we were forced to use "is". Which is the case in hindi.
Thats the long answer, the short answer is to just look for the hindi noun without any postpositions, thats usually the subject of the sentence and you can conjugate the verb according to that.
He - यह/वह
She - यह/वह
Him - इस/उस
Her - इस/उस
They - ये/वे
Them - इन/उन
Technically speaking, इस/उस is not him/her but everywhere the singular third person is used as an object rather than the subject, Hindi uses a variation of इस/उस, eg: इसके/उसके (his), इससे/उससे(from him), इसे/उसे (to him), इसमें/उसमें (in him).
Similarly for इन/उन.