The Freedom of Information Act 2000 applies to public authorities in England & Wales (there is equivalent legislation for Scotland). The solicitors will not be public bodies, so FoI will not apply to them. The only public body will be Her Majesty's Courts and Tribunals Service (HMCTS). They will have discharged their normal obligations through publishing the Probate Calendar (or equivalents) and the grants of administration or wills. HMCTS will not know the beneficiaries, so an FoI request to them will gain nothing, I suggest.
I believe I am convincing myself that there is no obligation laid on the solicitors in these two cases, other than the overall ones of Data Protection of their clients' information, etc. So the answer is therefore probably entirely in the hands of the solicitors - within those overall constraints.
That being so the rest of my answer is just gut feeling. In the case of question 1, unless you can prove a relationship under intestacy rules that is just as close as the beneficiaries (in other words, unless you can prove that you should have been a beneficiary), then you have no right to the personal details of those beneficiaries. The personal data possessed by the solicitors was never intended for distribution outside the estate process so cannot be used outside that process. I believe this is what Data Protection would dictate. I could be wrong.
Question 2 is interesting. The whole point of publishing wills is to make the beneficiary identification process transparent. As this will seems never to have entered the probate process, those rules do not apply. But I believe that the solicitors would be obliged to demonstrate that they have not missed any beneficiary out. However, I suspect that asking for a copy on any grounds other than believing yourself to be an omitted beneficiary, would not meet with success. Even if you do persuade the solicitors that you wish to check if you have a financial interest in the will, they could simply ask you to identify yourself and then say "No, you're not in the will" - and that would be the end of the story.
The publishing of wills and admins is not done for genealogical reasons - I suspect the solicitors would stick to the spirit of the reason for publishing wills, rather than the letter, and refuse to publish unless a will-related issue arose.
Most of the above is speculation on my part but I hope it is logical speculation.
Incidentally, I know of no limit that would permit a £7500 estate to avoid going for probate. The need to go for probate seems to be up to the bank or whatever holding the assets - they are at liberty to decide whether or not to require a grant of probate and at liberty to decide at what value the grant becomes mandatory. Again, it is possible I am wrong there, as both occasions when I have dealt with probate, the need for a grant was self evident so I may have missed a "Below £xxxx" limit.