Fuse the word showed up in the late seventeenth century from the word fusion, a mid-sixteenth century word from the Middle French fusion and classical Latin fusionem, outpouring, a noun version of fusus, the past participle of fundere, pour or melt. PS, fundere is also the origin word for found.
Interestingly enough, confuse showed up in the mid-sixteenth century (although it didn’t firmly take its place in English for another couple of centuries), while confused first appeared two centuries earlier. Confused was actually an alternate version of confound, in the way the classical Latin confusus is the past participle of confundere, to mix together (which is literally what con- plus -fundere means).
Showed up in the early fifteenth century from the classical Latin infusus and infundere, to pour in. Since -fundere is “pour” and in- is “in” (can you can puzzle out that one?), I’m guessing you see what I’m talking about.
First showed up in the early fifteenth century from the classical Latin diffusus and diffundere, which means to pour out/away. The prefix dis- means apart or away, so this is another straightforward one.
Showed up in the early fifteenth century. The classical Latin forms are, as expected, transfususand transfundere. The prefix trans- means across, so it’s “pour across”, or transfer by pouring.
Did not show up until very recently, in the nineteen forties. This means that unlike most –fuse words, it doesn’t come from Latin. It’s just a mix of the prefix de- with -fuse.
In this case, there are two homophones of the words, the verb refuse which means will not and the noun refuse which means garbage. No refuse showed up in the fourteenth century, in this case coming from the Old French refuserand Vulgar Latin refusare. The classical Latin equivalent is of course refundere, pour/give back, the origin word of refund. The garbage refuse comes from the Old French refus, waste, and comes from the above mentioned refuser.
Profuse (a word for large or excessive amounts), showed up in the early fifteenth century from the classical Latin profusus. Profusus/profundere has the same meaning as the English version as it’s a figurative way of saying “poured forth” pro- (forth) and -fundere (pour). Despite looking similar, profound, like a deep thought, has a slightly different word ancestry. Its suffix comes from the classical Latin fundus, which means bottom. Basically, fund is different from found and profound comes from the former.
There are also several other -fuse words that you may or may not have heard of, like effuse (pour out), affuse (pour on), perfuse (pour throughout), suffuse (overspread), circumfuse (pour around), superfuse (no longer used word just meaning pour) and finally, humifuse, which means to spread over the surface of the ground. Awesome points to anyone who can use it in a sentence.
TL;DR: fuse means pour and it’s related to found, but neither is related to fund.