I have a large figure with a long caption of 300 words, and they really don't fit into one A4 page. Can I enlarge the figure to fit in the first page and let the caption run to the next page?
300 words will be about 30-50% of the page. Such a large chunk of text seems substantial, so it's better to place it in the body of the paper.
In such situations, in the caption I usually just state what's in the figure, followed by "see text for details". And then I don't care if the text spills to another page.
This is not that unusual a situation. One sometimes sees a full-page figure, with the (full) caption on the facing page. I suspect this is less common than it used to be: back in the days where figures went on expensive 'colour plates', there was an incentive to maximise the area occupied by figure rather than text. I think it is less common to see the caption split across two pages (though this is sometimes done for footnotes, e.g. in humanities books).
As others have said, it is worth considering if you can reduce the length of the caption or reorganise the figure itself. However, it is not critical to do so.
No. Don't break a caption over the pages.
I am a fan of very explanatory figure captions. One to two sentences is fine. Figure captions are THE MOST READ parts of the text of a paper. Pay special attention to them.
But 300 words is WAY too much. I would keep it under 25 normally and never over 150 (which is a normal, not over-long, paragraph). You need to move some of that to the text.
But please don't say "see text" (this is too "duh"). Just have a flowing argument that the figure fits into. Oh...and still try to find a way to make the figure relatively self contained to view and read caption. (Challenge yourself.)
Also consider to have a couple (or more) different figures if you are doing too much in one figure, such that it requires so much explanation.
P.s. I am the normal guest. Cue Highlander...