Hi,
While using btc for small payments (< $10), standard costs already around $10 approx. 30 minute completion time. This is too much for small deposits for shopping purposes.
What do you recommend? Using any other crypto or how to find best off-peak hours to use? My transactions are around 12 hours with $1 cost

I just checked current state of Bitcoin mempool and fees are not $10 but more around 60 or 70 sat/vB that is roughly $5 or $6, but if you are not in a hurry you can use lower fees and wait for weekend confirmation.
My suggestion is to always use bech32 Bitcoin addresses starting with bc1 that will reduce transaction fee, and in future don't use Bitcoin for small transaction if you want to save on fees.
Maybe some second layer solution will solve this issue, Lightning Network is growing every day and I expect to see it doing this work of small transactions in future, but for now you may want to use some alternatives.