Yes, and you should. Any expense incurred after your HSA was established is still reimbursable, no matter how long ago.
Yes — backfilling is one of the most valuable things you can do on day one.
There's no rule that a receipt must be logged in the year it was incurred. The only requirements for a qualified reimbursement are that the expense was incurred after your HSA was established, was never reimbursed from another source, and was never claimed as an itemized medical deduction on your taxes.
So dig through:
Providers will usually re-issue an itemized statement for a past visit if you call and ask. That reconstructed paperwork is real documentation. A card statement alone is not.