Present participle

Hi, everyone.

I teach middle school kids who learn English as a foreign language. I myself have learned English grammar and all that but there are some doubts and misunderstandings in some grammatical matters.

To make it short, I'd like to ask for help with present participle,

We learn as :

(a) I have a difficult time (in) writing in English.

(b) I have difficulty / trouble/ (in) writing in English.

(c) I have trouble seeing.

Those two sentences, (a), (b), above mean the same and there is a preposition omitted, but some people say there's no preposition in the sentence (c).

If so, I don't know how to understand the sentence (c), and I'm questioning if it's relevant to the fact that the verb "write" in the first two sentences is used as a verb and and an object of the preposition whereas the verb "seeing" in the last sentence only as an adjective which modifies the preceding noun, "trouble."

If any of you know how I could get a deep knowledge of this, please let me know by leaving a link or information of some references. Thank you all in advance.