wave 2 starts when wave 1 ends, the timer is how much of a delay occurs between those two events. the timers run sequentially, not in parallel.
no, shooting down the carrier will start the timer on the drop mission, albeit at double the usual delay.
alien terror DOES work like that, but it IS different. the ufo spawns the terror site when it lands.
the way to achieve your desired result, apart from the multiple types in a single wave, is simple:
alienMissions:
- type: STR_ALIEN_DROP_SMALL
points: 3
objective: 3
siteType: STR_DROP_MISSION_SMALL
spawnZone: 3
raceWeights: &raceWeightsAlienDrop
waves:
- ufo: STR_UFO_PROBE
count: 1
trajectory: P1
timer: 15000
- ufo: STR_UFO_SCOUT
count: 1
trajectory: P1
timer: 5
- ufo: STR_UFO_CARRIER
count: 1
trajectory: P7
timer: 5
objective: true
please note: i have changed the semi-colon on the first line to a colon, in case you missed it.