Answering this step by step seems the most feasible.

Where would those localities get their money from? I doubt that there were 75 different gold mines in Switzerland which allowed each locality to mint their own currency. Could it be perhaps that they issue an order at a central gold mine to mint currency for them?

Predominant amount of gold and silver were mined in a handful of locations and then distributed, exchanged, sold and bought across much of the continental Europe, ranging down even to Italian cities, where minting was then done locally.

Why did each locality have their own currency?

This requires a broader view at first, namely as the result of terriotorial and jurisdictional fragmentation, and that minting was, or had the potential to be, a lucrative business. Often jurisdictions minted same coins nominally (like deniers), that nevertheless bore the name of the origin, since there were variations that resulted in different real value, thus Maine deniers had the few-fold value over some of the neighbouring deniers. France though underwent central minting regulation much quicker. Local currency also provided fiscal flexibility with currency depreciation, and the establishement of broadly two-tier currencies, for local (and small sum) and non-local (and large sum) usage. Thus a handful of well-known, valuable relatively stable currencies were used throughout Europe in banking, trading, etc.

Did there exist supra-regional currencies that were valid for more than one locality? Like an empire-wide currency for example?

Perhaps to add on what was said above to add complexity, degrees of centralization differed, and we have different ways of central regulation, whether it was exclusively under central authority, or whether there was regulation on coin characteristics. Futher, there were numerous monetary unions throughout this period (some continental cities, for example) that established their own norms for common currencies by the late middle ages and early modern period, which should equalize their nominal and real value, even though they still bore their local origin.

Another thing to mention here that currencies were regulated in a different sense to protect the local currency and trading reputation. We are speaking here about larger sums, naturally, as import of foreign currency was sometimes regulated (and cities, principalities, etc. anything with relative autonomy) had their own organs where it was under conditions of mandatory registrations, limitations and a tax, or subject to a penalty or foifeture. Further, most cities (jurisdictions) had currency crimes and asseyers (both official and private), which would inspect large sums of foreign/rareer currencies for weight and purity. This is all in very broad stroaks.

Could I pay with a different locality's money? If so, whats the point of each locakity having its own money?

Yes, there was no official or "exclusive" currency we know today. Places used local, more known neighbouring, and well-known "continetal" currencies, and they had real value (based on weight and fineness) and conversion ratios. As long as one finds a seller etc. who wished to take it, it was fair game. (With some conditions mentioned above.)

How would the value of my money be determined? Sure a Bern thaler and a Zürich thaler may both have a nominal value of 1, but maybe the Bern thaler has 50% more gold content in it. Or what if I have 53 gulden? How many thaler is that?

Beside nominal value was real value (weight and fineness) which was the basis for (relatively fluid, one may say) exchange rates. Yes, there are accounts of speculations and currency trading based on exchange rates, and how these exchange rates may differ locally. Sometimes, a neighbouring jurisdictions had different exchange rates, and sometimes some people took advantages of that until it was not corrected.

The last worry seems unnecessary. Coins were minted and reminted (and sometimes defacement and low amount of local coins with implied dominance of foreigh coins with same nominal value, but lower real value, were a reason for reminting, often with depreciation), low-value currency had relatively low and local velocity, with low export, high-value currency for trading just as often stayed in the city or returned for trading in the future, etc., by this time we also have banks, book-keeping, etc., so oft wealthier merchants or "institutions" had their local reserves. Crises did happen though, but we would need specifics for that.

I can address furher questions, and I will try to gather a reading list, English only, although as with most things on the continent, much of the literature (holds even more for specialized issues) would be in corresponding national languages.