What kind of grammar error this sentences have? 1) John gave the flowers to Mary and I. 2) Henry is the strongest of the two boys.?

pretty well the same type of error as in the primary question, a mismatch of case or number.

Correction #1: What kind of grammatical error DO THESE sentences have? (sntences is plural, and this is used only for the singular)

Correction #2: John gave flowers to Mary and ME (the pronoun is an indirect object, object of a preposition, thus ME).

Correction #3: Henry is the STRONGER of the two boys. (superlatives require more than two, comparative is used for two, a comparison of one to another rather than a comparison of one to many others).

John gave the flowers to Mary and me. 'Me' is the object of the sentence so you use the objective form.

Henry is the stronger of the two boys. When there are only two boys, you use 'stronger'. For three or more boys it would be 'strongest'.

John gave flowers to I? no, it should be ME. Strongest would be for out of 3 or more. Should be Stronger.