What are the right parameters to trim a small RNA transcriptome with trimmomatic?
The command where you trim with adapters and by quality is perfectly fine. That FastQC isn't perfectly happy is expected. It's a tool made for whole genome sequencing QC, you SHOULD see a number of "fail"s with any RNA-seq protocol. Steps that should always fail in RNA-seq:


per-base sequence content (there's "random priming" performed that isn't completely random, so the first ~8 bases show a typical bias pattern).
per-sequence GC content (particularly in sRNA-seq you're enriching for a subset of genes, they won't have some nice GC distribution and that's perfectly OK).
Sequence duplication level (if this doesn't fail then everything is uniformly expressed...which would be quite unlikely)
Overrepresented sequences (as above, though this will be worse for sRNA-seq since reads will often cover the entire transcript, so there's even less sequence diversity)