This is amplifier dependent. Almost all solid state amplifiers are stable into no load, but not all tube amps were.
Check with the vendor.
Yes! Almost all solid state amplifiers are stable at no load, except those without a Zobel network at the output!
https://www.diyaudio.com/community/threads/zobel-or-no-zobel.120748/
In _all_ cases you must ensure that the switches used are "break before make." That is, they open completely before making the next connection. The alternative, make before break, can be disastrous for any amplifier.
Depending on the design, a 3 position MBB (make before break) can be used with a dummy load to ensure that the amplifier is always connected to the load when switching.
If a speaker becomes disconnected (cat/dog/ferret whatever) while playing music and it's not noticed you have the same damaging scenario - stuff happens.
Installing a 100Ω 5-10W wire wound resistor on each channel of the tube amp output terminal is insurance against accidents.