@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 sehen
or 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 dieben
).
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).