Firmware updates are automatically downloaded when you connect to the Internet, but they are not automatically installed. If you don't install them, you can't connect to eshop, which may also mean that you can't play certain games online, if they need patches that you normally get from the eshop. Also, the 3DS keeps nagging you to install the firmware update every day or so. You can get rid of this nag (in real firmware) using the method at
https://gbatemp.net/threads/guide-delete-predownloaded-update-spotpass-nag.381489/ .
Gateway requires real firmware of 4.1-9.2. You run one of the exploits every time you boot the 3DS and it then puts you into EmuNAND, which is an emulated copy of a newer firmware, and you can run pirated games from that that need the new firmware. Gateway has to update their own launcher so that each new firmware version can be used as EmuNAND, so if they go out of business tomorrow you may not be able to play games that need firmware newer than the EmuNAND you already have.
There are two exploits. One is a web browser exploit which works with real firmware up to 9.2. You need to connect to a special web page to trigger the exploit. However, people have written Android apps that let you do this without really connecting to the Internet, so you don't risk downloading a firmware update at the same time. The other exploit is the profile exploit which is in system settings. The profile exploit requires real firmware of 4.1-4.5. You need to install this profile exploit using a DS flash card (the Gateway comes with one) and every time you run a DS game, you need to install it again. If you have firmware up to 9.2, there is a method to downgrade the firmware so you can use the profile exploit from then on instead. Neither exploit takes more than a few seconds to run.
Gateway lets you use as many pirated games as you can fit on your flash card. It supports 64G and 128G cards.
I don't know as much about the Sky3DS since I don't have one. It supports the newest firmware right now. In theory Nintendo could block it, but they haven't so far.