How can I track that this was satisfied by FAL request?
1.Do you set FAL parameters in your standby init.ora? ('FAL_SERVER' & 'FAL_CLIENT')
2.FAL is running on primary server. Check you primary database alert.log, you should be able to see some entries like: 'ARC0: Begin FAL archive','ARC0: Complete FAL archive...
3.If no FAL parameters set, ARCH also can automatically send missing archived logs to standby db.

Both the primary and standby were up and down during this period, but I never manually recovered anything.
Most of time, you don’t have to manually recovered/sync standby db as Oracle automatically resolves the gap issues. (oracle 9i)

I'm sure it was applied, but not sure how it was applied. The alert.log of the standby shows it was applied, but v$archived_log doesn't.
Again, it comes back to your original question. You may refer to oracle article '263994.1' for the answer.

I guess my big question is how can I verify all my logs have been applied without looking at the alert.log on the standby.
For me, I always query the max(sequence#) from V$archived_log in primary db to get the latest logs applied. Sometime I also need to verify it in alert.log if any doubt. As noted in oracle article 150214.1, you can’t trust V$archived_log 100%.

In article 150214.1---
'Note: the sql statements give additional information (confirmation)of information of alert files. If these sql statements return rows it doesn't necessarily mean ther's an actual gap! Always check the alert files as in 1b.'