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I.e lateral, nasal, and rhotic fricatives. These aren't very common sounds; do they tend to operate more as fricatives or as resonants? My guess is as fricatives, but I'm willing to be corrected,

These don't quite seem comparable to me. Lateral fricatives are rare, but I can think of a fair amount of languages with them. They often derive from earlier resonants, which means they might retain some of the patterning of this.

Nasal fricatives... what are you thinking of exactly; can you give an example language? From what I remember, there are languages analyzed with nasality as a phonemic feature of some fricatives like /ṽ/, but where the actual phonetic nasality mostly shows up in assimilated vowels.

And what do you mean by rhotic fricatives; stuff like /ʂ/ and /ʐ/?

I'm afraid that, by current usage, "resonant" and "fricative" denote two sets of mutually exclusive PoA, so they don't exist because definition  

However, the three examples you listed are slightly different so they can exist, to a degree.

"Lateral" and "fricative" are two discreet concepts, one is centrality, the other is PoA, so they can coexist. Their rareness, I believe, is due to languages generally having only one phonemic lateral consonant, the easiest of which is /l/.

Technically, nasal fricatives can exist as it's possible to create turbulence within the nasal cavity, however, they only exist in speech impediment as far as we know, there's no known reason why no language uses them. Nasalized fricative, on the other hand, do exist, although rare, possibly due to nasal release can take away too much airflow for fricative to sustain.

Rhoticity is a rather chaotic concept and there isn't a common trait shared by its members other than being orthographically <R>, i.e. rhotic fricatives are only rhotic because European languages uses <R> for them. If, say, the Chinese were as influential as Western European countries in the early days of modern linguistics, then [ʐ] would probably be a rhotic as well as it's in free variation with [ɻ].

Lateral fricatives I'd say are more often actual fricatives, but it depends on the language. Some don't clearly distinguish between fricatives and approximants in the first place, doing things like altering l-ɬ z-s, or allow the lateral fricative to voice or devoice more freely than either approximants/liquids or fricatives.

Nasalized fricatives I don't want to generalize. I think I've seen them pop up very rarely in Arawakan and/or Tupi-Guarani where they're clearly sonorant in nature, while in one or two Bantu languages I've run into them they're clearly fricatives, not sonorants. In Irish, unless I'm mistaken the nasalized /v/ shows both behaviors: it split into /w vʲ/, though both pattern as fricatives, but it also underwent vocalization.

The very, very few languages I've seen them in, fricative trills more clearly act as fricatives: they assimilate voicing in the Slavic languages that have them, and in Kobon the liquids are only voiceless finally but the fricative trill can be initially like the fortis obstruents.