2. Did you provide a detailed CV with form CF83? When I called the NI helpline I was told to include - CV including dates and locations, copies of HK employment visas, copies of employment contracts, P45 from last employment in the UK. It was an inch thick of paperwork. My claim was processed pretty quickly (compared to the usual wait - it was about 4 months, others have been waiting over a year) with no further correspondence with me required. I think I got bumped to the top of the pile as I'd made it easy for them. The offer I received for back payments was broken down in to a mix of class 2 and class 3 payments. Class 2 for my time working in HK, and class 3 for the time I was here job hunting and not working. You can select which years you pay, it's not all or none. I chose to pay the class 2 years but not the class 3. When you make the payments call them up and tell them how to allocate the payments.
4. The deadline to make back payments in respect of NI years more than 6 years ago is 2025. On an ongoing basis you can make back payments for the previous 6 years.
5. Between now and your date of retirement the UK pension is inflation adjusted (currently the triple lock rules apply). Depending on where you retire to it may or may not be adjusted annually in line with inflation. I don't plan to retire in HK, most likely will be Europe where it is inflation adjusted. Class 2 is a total no-brainer. Even class 3 is worth it according to most financial experts (google Martin Lewis voluntary NI contributions).
Yes you can 100% just pay the class 2 years. Just make sure you give them clear instructions on which years to allocate your payments to, and double check they do it correctly (via your HMRC government gateway log in). I have heard stories of them being allocated incorrectly, they can get sorted out but it's added hassle.
Also adding - it is a common myth that you need 35 years to qualify for the full state pension. This is only the case if you started working after 2016. If you started work before then you'll need anywhere between 29 and 50 years of contributions, depending on if you were ever contracted out of SERPS and for how long. I need 36 years but my husband only needs 30 (he's slightly older than me and was never contracted out). You can find out how many total years you need by looking at your future pension forecast, which is in a different section of your government gateway account than your NI payment record.