I don't have any idea on how this would impact on your offer *but* usually with any professional courses (including nursing) there can be major issues if you are found not to have declared things: not because of the conditions themselves, but because of the questions it raises about integrity. So I would strongly suggest, from that aspect alone, that you do declare these things, as you are likely to be able to do any damage limitation (if that's even necessary, which it may very well not be) rather than be stuck with explaining later why you with held the information you'd been asked for. Your GP can't disclose your medical records without your permission to OH/the university, but if you were asked to give permission, and refused, it might raise further questions for them. I really would be honest about your diagnosis and your medication: about your previous addiction, I would personally only disclose that if specifically asked (or if it was likely to be referenced in some way on an enhanced DBS check) - but if they ask, definitely disclose this too (to avoid them finding out later, and it damaging your chances of being able to proceed with studies/career).
I would also suggest disclosing your diagnosis from an Equality perspective: you fit the Act's definition of someone with a disability, and this actually gives you additional protections if you tell the University - and also enables additional support to be put in place to help you complete your degree successfully too. It's very much in your best interest to be about up front for this sort of reason, not only because of the additional protection but also because there may be reasonable adjustments they can put in place as well.