It's fine; see what Ed says. What Ed is saying is that a circuit serving 120V loads on both legs and also 240V loads is perfectly fine, as long as the circuit breaker has "common trip". That's so if 120V loads trip one leg of the breaker, the whole circuit gets knocked out - if you left the other leg energized, power would leak into the tripped ...
It sounds like you have a multi wire branch circuit, these were more common prior to the requirements of GFCI’s.
NEC 210.4.C states to supply line to neutral loads.
however exception #2 comes into play when all ungrounded conductors are opened simultaneously by the branch circuit over current device.
Then exhibit 210.2 shows a duplex 240 / 120 receptacle.
Yes and no. It not as simple as keeping the wattage under the maximum value.
The load needs to also be balanced if you have 120v devices the load needs to be on both legs equally or close. 220/240v loads are usually balanced but not always. (A dryer is a example of an unbalanced 240 load).
1 120v leg you can normally pull 2400w beyond this will probably ...
Yes you can provided that you don't exceed the wattage ratings.
Smaller generators have a selector switch and you have to decide whether you want 120V or 240V but the larger ones let you run both voltages.