In my opinion:
spec. is for genera
indet. is for higher taxon levels.
I don't know where these basic rules hail from. But I am very sure this is the proper way. (check out any scientific paper).
Also note that species and genera names are to be written italic; higher-level taxa are not to be written italic. The abbreviations "spec." and "indet."themselves, should not be italic.
agg. and s.l. are not identical.
agg. = aggregate of species, such as problem species groups which cannot be identified to species level as larva but only as can be id'd to species level as adult, like some Chironomidae;
s.l. is sensu lato, in the wide sense (as opposed to s.s. sensu stricto). That typically applies for species which have been split up: if you want to stress that you found a specimen of a species which has been split up, and you are sure it's not on of the newly described species which originally was not split up, you may want to use [species] s.s.; if you are talking about specimens before the split, use s.l. (just check Wikipedia on this
https://nl.wikipedia.org/wiki/Sensu_lato)
In short, we should retain both agg., and s.l. We could also retain 'complex' , but that's generally not liked any longer. We better avoid that (there is no added value retaining 'comlex'.