yes but in 2020 and during Covid so things might be different now.
My wife had same extension of stay as your wife and I was working and had extension of stay based on employment. My wife's future employer liaised with my employer at the time in order to get everything that was needed and ensured that my wife's extension of stay wasn't cancelled until they had all of the paperwork in place.
Note as travel overseas was very difficult in Q2/Q3 2020 this was all done within Thailand, including her getting herself sorted so she could work legally in Thailand.
correct, if he didn't have a non-immigrant visa then he would be asked, that being said I know of someone who has a work permit who the airline in PH refused to let board until she bought a flight out of TH at check in. In that scenario, the check in in PH were wrong and she should've stood her ground and refused.
they're ultimately responsible should immigration in Thailand stop you from entering. Some airlines are stricter with onward departures than others but just saying you're leaving overland might not work.