are these sentences grammatical/ make sense?

To me — Yes! Don't you understand their meaning?

I don't think that 'I am insulted' is grammatically correct when you look at the sentences definition. Am I correct?

I (subject) am (verb) insulted (adjective)

or

I (subject) am insulted (verb in passive voice).

What is it that you think disagrees with the definition of sentence?

Below are all of the definitions that Dictionary.com gave for 'insulted'.

1. To treat with gross insensitivity, insolence, or contemptuous rudeness.
   
2. To affront or demean:


And according to the defintions, 'insulted' is an action verb. That's why I don't see how it could work, and why I think that you have to use 'feel' before 'insulted' for the sentence to be

Both are correct, but different.

Feel and bedon't mean the same. Look in a dictionary