Software level airgap - you have turned off your WiFi in your OS.
Hardware level airgap - you have physically removed your WiFi card (or never had one to begin with).
I think both are very secure, but software airgap has 2 possible flaws:
1. software malware like the one you mentioned in the answers above.
2. it's just one click away from becoming "non-airgapped". I think this has also been mentioned somewhere above.
In any case, yes, hardware level airgap is not so prone to errors.
If you are under threat of attack, i.e. live in a 100-unit apartment where god knows who is your neighbor or your neighbors' guests, believe me, you can be in trouble. If you live in a single-family home and your neighbors and your area is a very safe area where strangers don't move, then to my mind, software airgap alone can't be an issue. But as o_e_l_e_o pointed, software level airgap will always be less safer than hardware level airgap and I suggest you to stick with his advice.
Answer to your questions:
1. If your computer has never been connected to internet, you won't have software malware unless your manufacturer already gave you an infected computer, i.e. you can't do anything if there exists hardware backdoors in every modern equipment. To be honest, I am afraid, as science and technology develops, the higher the hardware backdoor chances will be. That's why I prefer to use very old device.
2. If there is no wireless signal in your area, just one click can't make your device non-airgapped. If you are absolutely alone in 2km radius and you have an Wi-Fi with password, I don't think your computer is going to hack the password. Absolutely every advice should be suited to individual threats and possibilities. If you are under a serious cyber attack threat, then simply air-gapping your computer is not enough, you need to isolate the room where your computer is located, block all wireless signals and use a Faraday Cage.