Learn Dutch: Zij vergeeft de betweterige suggestie. - She forgives the know-it-all suggestion.

It comes from the noun de betweter, which literally means a "better-knower" (a know-it-all). To turn this noun into an adjective, we add the suffix -ig, making betweterig. Finally, because it modifies the de word suggestie, it gets the standard -e ending, resulting in betweterige.

Why is there no person mentioned with the verb vergeeft here?

The verb vergeven (to forgive) can take just a direct object for the thing being forgiven, exactly like in English. If you wanted to specify who she is forgiving, that person would act as the indirect object without a preposition. For example: Zij vergeeft hem de betweterige suggestie (She forgives him the know-it-all suggestion).

How could I connect this sentence to a Niet dat clause to prevent a false assumption?

You can use a Niet dat clause to clarify that her forgiveness doesn't mean she liked the suggestion. For example: Zij vergeeft de betweterige suggestie, niet dat ze er blij mee is. (She forgives the know-it-all suggestion, not that she is happy with it). Remember that Niet dat introduces a subordinate clause, pushing the verb is to the end.

How is the -tie ending in suggestie pronounced?