Whats the name of "this" country? If you are not a visa national as stated, you only need a passport & probably a birth certificate (which may not be requested at border at all).
If all your previous leave applications were made on time & you have not been away for longer than required then you should apply for ILR (LR). You will need to provide all your passports to prove residence. Any rejection should not result in your existing leave being revoked.
Have you tried asking them to manually enter bar code number? I would try another post office just in case if might scan there before contacting HO to send another letter.
No you won't be trapped. Use NCS or NDRS from your local council & you will be able to keep your original documents including passport & BRP & you will be free to roam around after enrolling bio metrics.
It is applicant's responsibility to make sure they are aware of the requirements. You are not allowed to present new evidence on appeal. If you are unsure of anything, seek professional advice.
You should be getting an invitation to book ceremony with the council shortly. It can take from few days to upto couple of weeks in some cases but there is nothing you can do now, sit tight and relax.
If you have sent them required proof that you were in the UK legally all the time then you can't do much except to wait now. Did they mention in their letter that by what date they need the questionnaire back?
You would need some sort of proof in that case, they may well or may not choose to ignore discrepancy in your passport stamps. You surely would have something like bank statement, utility bills or pay slips etc if indeed, you were present in the UK during the period when your passport was not stamped.
You can the. Carry on keeping this PR and it should be no no problem. UK will most likely change your PR into something like ILR in the future so it’s all good.