BE and DO have two principal functions in English. First, BE and DO are both auxiliary, or 'helping" verbs. They are each used to provide the tense (and sometimes person) marking for main verbs, as in
1)]Is your sister working or going to school, or both?
2) Does my translation make sense?
But BE and DO are also main verbs themselves, as in
3) Where is your homework? It's due today.
4) You did a wonderful job on your report this time!
Now for your sentences:
When is the movie?
IS is a main verb here, not an auxiliary.
When does the movie start?
DOES in this sentence is only an auxiliary, the main verb being START.
*Whendoes the movie?
This sentence is incomplete. DOES here is only an auxiliary, and needs a main verb to complete its meaning.
*When is the movie start?
IS (BE) can't be used as an auxiliary with the base form of the main verb, START. The verb form would have to be STARTING:
When is the movie starting?
(In conversation you often hear something like:
When's the movie start?
The "s" sound in the contraction is not the "s" of IS. It stands for the auxiliary DOES.)