Yes, you are right that it is the following pattern:
"I have trouble +doing+something" and all your examples are fine:
1) I had trouble facing the problem yesterday.
2) I'll have trouble making them better in the near future.
3) I have trouble surfing this web side.
4) I have trouble taking part in tomorrow's meeting.
Please note the error in #3: it should be "WEBSITE"(one word,"site(=place) not "side").
Don't forget there's also this pattern: "to have trouble +WITH+something", e.g.,
"I'm having trouble with my car."
"I had trouble with the copier."