I was wondering, where would the indexes be stored? If I search "blog post about cats", where does it search the forum posts about cats?

Also, if payments can be done, that would be awesome, though it seems that is not something Matrix is trying to achieve?

search isn’t a solved problem yet. you could search your local server, or spider your neighbours, or build some kind of decentralised search engine. it’s the same problem for Matrix in general; we tend to cheat and just rely on Google to have indexed everything for now :)