Looking for language study partners (Because it is a title you can drop the subject but if you write it out fully it is "I'm looking for language study partners". Because you are still doing this you want the progressive tense which uses the "ing".)

I'm new here. My name is Jon Chai. I can speak mandarin. I'd be happy to teach you Chinese and introduce you to my country, China. I'm also interested in improving my English. I hope to find some friends at here. If you want to make friends with me, send a massage. I think we will be good friends.

Keep in mind:

Periods go immediately after the last word in a sentence and are followed by a space.

I'd be happy [infinitive] + [object] - this is a fixed phrase and is followed by a verb in the infinitive form ("to teach", "to help") and then an object ("you", "him", etc.).

I made more mistakes than I highlighted but just focus on what I highlighted. You are learning and should take it one step at a time.

-Ben