I think at is your best choice; that's the preposition usually used in that context.
More specifically, I would use at, because we usually say at all levels:
I have student-teaching experience at the high school level.
It may be worth noting that, at least in the U.S. educational system, all of high school is considered one level, consisting of four grades. So, this is the way I'd recommend saying this (depending on what grades you taught):
I have student-teaching experience at the high school level. [i.e., I taught students in grades 9 - 12]
I have student-teaching experience in all high school grades. [i.e., students in grades 9, 10, 11 & 12]
I have student-teaching experience at both the high school and middle school level. [i.e., students in grades 9 - 12, as well as students in grades 6 - 8]
However, that might be different in other countries.
One other thing worth mentioning: when we use a past tense verb with the phrase "in high school," that usually indicates an activity we did as a student.
I took geometry in high school.
So, I would avoid, "I had my student-teaching experience in Chattanooga High School" (even though it's not grammatically incorrect), because that could be interpreted to mean that you did student teaching while you were a high school student. It would be much better to say:
I had my student-teaching experience at Chattanooga High School.
The usual wording is
He knows English at a basic level.
Both of your wordings are easily understood (and difficult to misunderstand), but are not those of a native English speaker.
Best Answer
Level can mean two things - how something measures against a scale, and a platform one stands upon.
If by "level" you mean "how high, how much," at is used. Think of a scale, like that on the side of a measuring cup, and with this use of level you are asking where the thing you are measuring lies on such a scale. You would typically use the preposition at when answering where.
If by "level" you mean a platform one stands upon, on is used.
Also, @MrTheWalrus is 100% correct, on a certain level is an idiom and should be treated as a special case. So is on the/that/a same level:
This is an informal (if not slang) idiom that means the two people here had a mutual understanding about something, likely not explicitly spoken.