1. Forward is a noun, adjective, adverb and a verb,. Forward is a noun. Forward is a verb.

2. Since “look forward” is a phrasal verb the correct present continuous form is “looking forward”, not “looking forwarding” Is the sentence you mentioned grammatically incorrect?

3. I too look forward has been used since 1836 as a word like “I’m looking forward”. I look forward is more formal than “I’m looking forward” in formal letters.

Good luck.