Given the example:
I have trouble speaking English.
Can we use both present participle (speaking) and to-infinitive (to speak) after have trouble? If both are allowed, do the two have the same meaning or not?
No, you may not use the to-infinitive after to have trouble. You may only use the -ing form. You can think of it as an abbreviated version of this:
And for the most part, to-infinitives make poor objects of prepositions; for that were gerunds invented.