Hi,
I don’t think your question can be answered in such a general form beyond “we think hard and try stuff out” :-) Everything beyond this is model specific, so sharing your model is preferable (possibly in a new topic with more descriptive name). Divergent transitions - a primer has a list of hints for degenerate models (the causes of divergences have substantial overlap with causes of high Rhat).
That’s very likely correct.
That’s a likely possibility (the keyword would probably be “multimodal” or “non-identified” or “label switching” for mixture models) but a lot of other stuff can be happening, especially if you have increased adapt_delta or max_treedepth above their defaults.
Best of luck with your model!