Hi Rima,
This isn't an exhaustive answer but here are some thoughts.
My first question is aside from heatmaps and differential abundance testing, and looking quickly at the taxa-barplots that I’ve generated, what other analyses can I do?
The first thing that jumps out to me is looking at beta diversity plots, if you haven't already (not sure if this was included in the diversity analyses you did) -- in my opinion these are most useful as a diagnostic of "broadly, how different do these samples look?" and it sounds like this might be useful for your dataset. If your samples are all clustered together, then it may make sense that there wouldn't be very clear differences in later analyses like differential abundance.
I can't think of anything else off the top of my head that would be useful for your particular project, but I'm sure other folks on here (or some of the tutorials in Andrew's post) might have ideas. (Usually I'd recommend checking out some of the functionality in q2-longitudinal, but since your dataset has just two timepoints per sample I'm not sure much of that functionality would be meaningful for it.)
My other question is: I’m not sure which differential abundance testing to use. I tried to use ANCOM (which showed no significant differences) but as I understand, there are many different algorithms including songbird, qurro, aldex-2 etc… Is there a paper that you can refer me to that compares the different methods?
There have been a lot of papers back and forth on differential abundance tools. One recent one is this preprint -- there was a lot of discussion on twitter about it, and it looks like they just updated the preprint based on this feedback to consider some new methods (including Songbird). It may be worth checking this out. (That being said, I just read over the way they ran Songbird [without tuning the regression parameters], so I'm not super confident their results for Songbird are very useful.)
qurro
Qurro isn't really an algorithm so much as a visualization tool -- it should be usable with most differential abundance tools' outputs (of the tools mentioned so far it's mostly been tested with Songbird / ALDEx2 outputs, in particular).
I tried to use ANCOM (which showed no significant differences)
Although I've heard that ANCOM can be overly conservative with assigning "significance," it's worth noting that there really could just not be substantial differences between your sample groups (although one of the groups had lower diversity, I'm not confident that this means that there must be some "significantly" different taxa between the groups). This is a situation where beta diversity plots can be useful -- if there is a noticeable difference in how your samples cluster in one of these visualizations, then that could be something worth looking for ... but if there isn't, then it could be an indication of your samples having mostly similar compositions. (This is all kind of hand-wavy, the main point is just to suggest that the boring result [the samples are mostly similar] might be the true one.)
Also, is there a method that can test whether aggregates of taxons are more or less abundant in a clinical group over another. I know that Gneiss can do that, but it’s no longer recommended?
I think PhyloFactor may be useful for this? It isn't available in QIIME 2 though as far as I know. (cc'ing @mortonjt.)