Is the construction "to be fine/okay with doing something" grammatical and common usage? Example : "I am fine/okay with waiting." I always thought it was and I have heard it a few times but couldnt find it in any dictionary. The only thing that came close was the expression "That is fine with me." (which there already is a question about but I dont think its quite the same as this one right here)
"I'm OK with that" and its infinite array of variations are colloqualisms commonly used in spoken English. I personally catch myself using, "I'm good with that," to express my permission, blessing, or acquiescence to a decision.
However, I suspect you'd find a bit of argument over whether or not it's grammatically correct. In formal "book" English, the idea would be phrased, "I accept that decision" or "I am happy to complete that task." In these cases (and in the colloquial cases) we are expressing an affirmation (or much less commonly, a negation), often using an appropriate emotion as a metaphor for the affirmation.
An amusing cultural case is the phraseology of the "Jive" dialect popular in the U.S. during the 70's. The common phrase then was "I'm down with that," probably derived from the phrase, "get down!" I'm afraid I would need to perform some research to explain exactly how that phrase came to be, but I assume whole books have been written in an attempt to explain how (and why) Jive exists.