Translation:Do you like watching movies?
This is probably where they will have so many issues with translations tjat should work but are counted as incorrect.
Watching, to watch... In English, either one is fine in a sentence like this. Having to memorize which one duo insists on interferes with remembering the Japanese.
It is hard to explain why. It should be a valid answer too, but to be precise, a direct translation to "do you like to whatch movies?" would be 「えいがを見ることが好きですか」Adding "koto"「こと」after the verb will change it to its equivalent infinitive form in english. For example: He eats sushi =「かれはすしを食べる」and He likes to eat sushi =「かれはすしを食べることが好きです」
I commented on something similar to this in an earlier question, but I think it's misleading to define ～すること as the translation of the infinitive form.
Using your example, "He likes to eat sushi" (infinitive) and "He likes eating sushi" (gerund) have essentially identical meanings in English. Likewise in Japanese,「 彼はすしを食べることが好きです」and「彼はすしを食べるのが好きです」are essentially identical, and you can't assign one to the gerund over the infinitive.
Pronounced "wa". It means "as for".
"As for watching movies, do you like it?"
That's your topic. That's the general / most important thing you're talking about.
"Ga" is a subject marker and is ridgedly grammatical. As such, I don't think it can attach to the gerund "watching movies" because that is not technically a subject. A subject performs an action. With "watching movies", the action - to watch - is already in there.
You're right that が is a subject marker, but it also has other roles. が can be used to mark the complement, or the target for ability or preference. In this case, 「映画を見るのが好きです」 is also grammatically correct.
は is special particle, in that it can supplant other particles, fulfilling their roles and mark the topic.
If えいがを見るのが好きです is grammatically correct, then why is えいがを見るのが好きですか incorrect?
It should also be correct. However, using は over が is typically preferred for general questions (i.e. not follow-up or confirmation questions) in order to add emphasis on the thing you want to know about.
I was so close to typing うん、好きです