@AndreKRs Link explains most of your question.
This will work with all verbs (but not only verbs, some examples are in the link), but from my experience, is mostly used when you do something from time to time in an unprofessional manner. So you can't really use it with words like
hören, because these are not activities that can be done "well" or "badly". The sentence
Seine Diebereien werden ihn noch ins Gefängnis bringen is not something you'd say about a professional thief, it would rather make you think of a teenager who steals from time to time but lacks professionalism. (Also, this is an example where a noun is treated this way, there is no verb
So the connotation is almost always "not well done" which would make it negative.
Often, they are prefixed with "Herum". I'd always prefer
Seine Herumputzerei hat den meisten Dreck übrig gelassen to
Seine Putzerei ....
There are some words, like
Wäscherei, which are used for a place where something is done professionally (a
Wäscherei being a shop where you can get your clothes cleaned; although this word seems a little antiquated and has gotten replaced by
Reinigung). In this case,
Wäscherei has no negative connotation, but i might still say something like
Die (Gesichts-)wäscherei meines dreijährigen Kinds hat alles nur schlimmer gemacht. So depending on context, the same word may have different meanings.
Sauen, derived from Sau (female pig), is a south german/bavarian/austrian verb which means "make something dirty". I don't know if the verb got in dis-use in northern germany, or if
Sauerei made it to north germany but
Sauen did not, but i'd assume there is the link (i'm not an expert though).