Hi, i'm Alex.
I'm learning Chinese and looking for a native speaker with teaching experience to work with.
I have experience of teaching English to adults and adolescents.
Please contact me.
我有英文老师经历。我教过大人和青少年。These sentences are not wrong per say, but compounding them into one sentence would streamline things.
Here's a preliminary revision.
Unit/ counters: "一个" is not wrong when you are counting human beings. "一位" is used in a formal-ish setting, implying his/her position is respected. For example, [他是一位很有名望的医生。 He is a very well-known and well-respected doctor.] Traditionally, Chinese people respect 医生，老师/教师，科学家，工程师。 （an example when 一位 is not used: 一位流浪汉 a homeless person)
talking about one's preferences: In a formal hiring setting, it's common to see a bullet list like 岗位要求/招聘条件， and the preferences would be written in the boilerplate form like "有xxxx经验者优先"、“有xxx以上经验者为佳”。When you are not doing a formal/official hiring, it is important to be direct, but not coming off arrogant. "Chinese should be its mother-tongue, and I hope it better has some teaching experience" can sometimes sound a bit 不庄重。
Overall your paragraph is well-written, I'm sure you can find a great teacher soon! Good luck.
I would like to be your language exchange partner.