My two cents:-
Scenario 1: It will only recalculate if you enter (+execute!) the new speed into the FMC descent page. As you say this will likely leave you high on your 280kt profile, and probably high on a 250kt profile since that would naturally be shallower. Enter the new speed and see how high once you have finished decelerating (if you have time). Then use drag to get back on the profile. If you don’t have time (maybe the constraint is fast approaching or you are too low to justify going ‘heads down’ into the FMC) then just speed intervene and get the drag out straight away and eyeball it!
Scenario 2. Assuming you are in HOLD | ROLL MODE | VNAV PATH, when you speed intervene the autothrottle will remain in HOLD when the pitch mode changes to VNAV SPD. As you accelerate you go below the profile. If you don’t use speed intervention, when you enter the new speed into the FMC it will recalculate the profile, this time likely leaving you low. THR | ROLL MODE | VNAV SPD should be the new FMA with THR targeting 1250fpm to regain the profile. My preferred option is using V/S for a short time to maintain present rate of descent whilst accelerating. Then enter new speed into FMC, recalculate, then back to VNAV to regain profile as above.
It wouldn’t drive to the fix in VNAV ALT, but go from VNAV SPD to VNAV PTH to satisfy the constraint. It will only go VNAV ALT when levelling at the MCP altitude.
As far as busting the constraint - only if you use basic modes. Quote from FCTM Ch 4, Descent Constraints: ‘the selection of a pitch mode other than VNAV PTH or VNAV SPD for descent will result in a risk of violating altitude constraints.’ Note this is specifically referencing the ‘Alternate MCP setting procedure’ for closely spaced constaints. The normal procedure is to keep the constraint in the MCP (in your example FL150) until the constraint is ‘assured’. A bit annoying depending on where you are in the world and how the descent clearances are phrased there! This is where some ‘resilience’ may be required…