Different TR doesn't really matter (that relates to number and thickness of slices, and acceleration factors like parallel imaging and multiband) but the TE is very important. Generally, lower TE equates to more signal and potentially shorter echo spacing. Hence, it is not recommended to compare datasets acquired with different TEs.
Note that higher multiband factors (hence much lower TRs) will lead to lower SNR, so that is something to be aware of.
One way to deal with it is to scan some subjects on both protocols and then compare them to establish the difference(s) between their data e.g. FA, track density, etc.
There are some articles on this. Do a pubmed search with keywords like "harmonization diffusion mri".
You can't easily do so unfortunately, different TEs also means different relative T2 weighting in your data, and hence potentially different results (and also gradient timings). It can be seen from the general signal equation, see wikipedia for example https://en.wikipedia.org/wiki/Diffusion_MRI#Mechanism
That also means your metrics derived from dmri will be slightly different simply because of the timings. As suggested above, there's been a few recent things about these ideas, but no clear cut solution for varying TEs as far as I know.