The mature products of the dominant arm (3p) for hsa-miR-101-1 and hsa-miR-101-2 are identical. Thus, if you had separate quantifications for each, in theory you should be able to sum them. However, as their sequences are identical, its difficult to know how you could have separate quantifications for each, unless the thing being quantified is not the canonical mature 3p arm. Quantification pipelines that consider both must be doing one of two things with reads that map to both (which should be the majority of reads): either they add a count to both, or the add a count to neither, or they add a count to one at random. If they add a count to neither, or they add a count to one at random, then you should be fine adding them together. However, if they add a count to both, then you should not add them together, but just take one or the other.

miRNAs that come from the same family produce mature sequences from their dominant arms that have the same seed sequence, but are not identical across the rest of their sequence. So, for example, hsa-miR-190a and 190b:

ugauauguuugauauauuaggu hsa-miR-190a-5p
|||||||||||||||.......
ugauauguuugauauuggguug hsa-miR-190b-5p
 ------ 6mer seed
------- 7mer-A1 seed
 ------- 7mer-m8 seed
-------- 8mer seed

We don't fully understand miRNA targeting, but we do know that the seed region (roughly speaking bases 2-8) are very important, however, the 3' end of the sequence can contribute to targeting sometimes in some yet to be understood circumstances. Thus miR-190a and miR-190b likely have similar, but not identical target sets. In fact, many target prediction algorithms might predict the same target sets (although I believe that recent versions of TargetScan do take the 3' end into account).

Just to complicate things the non-dominant arms may well have completely different seed sequences, and therefore target sets (as is the case for miR-190a/b).

You are correct that if a source has only miR-373 then it is only referring to one of the -5p or -3p arms, generally the more stable one. You can find this information at mirBase. The record for the precursor will show the balance of mature reads found for the -5p and -3p arms. The record for the mature sequence will have an field called "previous IDs" one of the two will generally be listed as miR-XXX without the -5p or -3p. This is usually the dominant arm.