Yes, check "Firmware status" pinned.
No. Such approach needs unreleased "Deja Vu" exploit.
Yes, you can do it manually on a game backup data and it's already included in Tinfoil and Goldleaf installers, but it has it's limits: there is a FW game "wants" and a FW it "needs". Installers can trick this check, but if you have FW lower than game actually needs, it will not start. And I don't know if they work on 3.0.0, maybe you will be sticked to devMenu on 3.0.0, which is user unfriendly.
You are on a fence with "only once". If you are going to use exploits, you will want a NAND backup. If you have a backup, why don't you go further and update to 6.2.0 with ChoiDujourNX (thanks rajkosto for this possibly useful tool) and autoRCM, setup Kosmos, add nogc patch to ini and go wild offline... with an option to go back to 3.0.0? If Nintendo will manage to detect a fact of RCM usage, your unit is done anyway, but you will be able to enjoy the stuff right here and right now.
It is my understanding that updating after the backup would blow efuses and thus make recovering the backed up nand potentially problematic. Additionally I am very much hoping for a way to do things without a pin jig or paperclip (other than for a one time backup like I said). Can't be done yet?