Hi Bastian,
I hope you’re doing well! I’ve just noticed you contacted us a bit earlier about our stroke studies; I’ll get back to you on that as well. We’ve learned quite a bit in the meantime about lesions with (likely) underlying vascular origins. Happy to share some insights.
About your current questions: I think one of the main things to realise is that the choice of using ACT or not is relatively independent of having used SS3T-CSD earlier on in the pipeline. The only connection of sorts is the fact that “out of the box” tractography will look a bit nicer and appear already more constrained to regions where it should go (and less / not in those where it should stay away from) when using SS3T-CSD versus using only single-tissue or 2-tissue modelling. I’m guessing this property might be what had you wondering whether the anatomical constraints are “already taken care of”; but it’s a separate thing in principle. Whether to use it or not, likely depends more on what you want to pursue afterwards. So your questions aren’t redundant; although I think you came into this from a different angle maybe. I’ll address a few things just briefly:
So this depends on what you want to do with the resulting tractogram afterwards. If it’s e.g. connectomics, where it’s often important streamline endpoints hit the cortex, etc…, then typically yes, you want to use ACT. If it’s e.g. targeted tractography of specific structures, because you want to analyse particular bundles, etc… then often no, you don’t need ACT. In the latter scenario, you’re likely already yourself imposing the relevant anatomical constraints by means of your inclusion / exclusion / … regions for tractography. If that’s already doing the job, then you’re good. This is important to realise, as in the presence of lesions, you might actually face unique challenges in using ACT. This is a bit too much to write all down here, but some of it at least relates to other parts of your post, so read on below. 
Well yes and no. These things are quite separate in some ways. Yes, it does make the WM FOD out of the box more specific to actual WM, and that’s a great thing for tractography. E.g. in cortical GM, the WM FOD will be much smaller, in line with reduced axonal density. The other GM signal from neuronal cell bodies, etc… ends up nicely “out of the way” in the GM compartment. So the presence of other tissues in the model improves the WM FOD, which greatly helps tractography. But it doesn’t perform an anatomical kind of “constraint” mechanism directly in the tractography process. So basically: it’s 2 different things. In lesions, we have used the SS3T-CSD approach as a diffusion signal representation rather than a biophysical model; e.g. for stroke you’re likely aware of our very recent work looking at lesion compositions. This is also great, because again WM FODs will decrease according to (e.g. reduced) presence of axon density, when infiltration of other tissues and fluids happens. But also, the WM FODs in all those regions will still retain nice angular structure because signal from other tissues is filtered out (and thus doesn’t “pollute” the WM FOD). Again, you’re set up with great WM FODs out of the box here as well, benefiting tractography but even other algorithms like registration, etc… greatly.
ACT depends on the quality of the segmentations (i.e. the 5TT map) that it uses. It then applies a set of rules to this, e.g. streamlines not allowed to stop in WM, streamlines need to end in / at GM, no traversal of CSF, etc… But herein lies the challenge: you need a good 5TT map. There are different ways to obtain this, but you should take a very close look to what your 5TT files look like out of the box in the lesions in your data. Because intensity-wise lesions are often in the range of GM or even CSF on a T1w image, several image segmentation algorithms might segment these as “GM” or “CSF” accordingly. That will then cause a problem in ACT if you don’t fix that up: if a lesion is labelled “GM”, ACT will treat it as GM, and thus make streamlines stop at the WM-lesion boundary. That’s likely the opposite of what you want. That’s why the pathology class exists. Again, read on. 
Well, so likely you then need to actually use or create volume 4 (the 5th volume).
No, I think you have the wrong idea about what the volume 4 / pathological class does. So out of the box, you’ll likely have volumes 0-3, coming from e.g. 5ttgen. First have a look at all of those in regions where you have extensive WMHs present. As I mentioned above, I’m guessing maybe some WMHs show up in the “GM” segmentation. So just applying ACT out of the box like that, will cause the issue I mentioned above: the algorithm will apply the rules of actual (e.g. cortical) GM to lesions. However, you likely want it to be treated as WM, because it is WM. A WMH doesn’t make it non-WM. 
So you could either fix all of that up manually (or e.g. using some lesion segmentation tool to aid this) and remove those bits again from the GM image, and add them again to the WM image. That would fix everything in principle. If you were to not do that, but rather draw those lesions in volume 4, what happens during tractography is exactly this: in those particular regions, the ACT rules just get switched off. But this doesn’t affect the WM-FOD amplitudes at all, so you retain the full quality and amplitude of the FODs you obtained from SS3T-CSD. Also, the other tractography constraints and settings still get applied (e.g. your curvature threshold, etc…). So again, these things are mostly separate. However, you’d have to be extremely precise in segmenting those lesions, and maybe even dilate the segmentations a bit. If they’re even only a little bit “too small”, you’ll still have “fake” GM on the edges of lesions, and most of the problem still remains when streamlines hit that “fake” GM. Same thing for punctate lesions or e.g. other small de novo lesions. So it’s a bit of a nightmare to get the precision right! That’s why you have to carefully consider whether your application requires ACT.
No problems there; SS3T-CSD will likely work well. On the ACT side, 5ttgen typically works with a T1w image. Finally, you certainly need a means to correct for EPI distortions if you need to perform ACT using a 5TT image derived from a T1w image.
I hope that helps. I’ll get back to you on the email; those questions are a bit more complicated. 
Cheers & take care,
Thijs