Translation:I like romantic movies.
If 的 is used, isn't then 浪漫 a noun meaning "romance" and the whole 浪漫的电影 phrase is literally "film of romance"?
浪漫的电影 actually is not identical to "romantic movies" in English, IMHO. Romantic movies refer to those with a love story, and the equivalent should be 爱情电影 or 爱情片. Although 浪漫的 means romantic (more precisely it is actually loaned from the word romantic), it does not necessarily limit to love stories. Some people may find the cowboy films of Clint Eastwood 浪漫的.
There is no "很" that I can see here; maybe you're confused with "浪" in "浪漫"
No it is not necessary. That thing only applies to a predicate.
It is even not usually added in this position, just as we seldom would say "I like very romantic movies" in English.
why not 'a romantic film'? in UK English usage singular and plural in this context mean the same.
That's fine, or even "the romantic movie" (in the context of someone deciding between one or more movies of different types)
Correct translate may be 我喜欢爱情电影.'Cuz romantic means 浪漫的or言情(a type of novel),you guys may know it.
Are there two pronunciations for 电影. When you click on 影 he pronounces it ''yin'' , but when he says the whole sentence he pronounces ''yang''.