Learn English – ny improper or awkward usage in this sentence

In a tear (or on a tear) does appear in OED:

3b. A spree (U.S. slang).

1896 Harper's Mag. Apr. 775/2 Got me off on a tear somehow, and by the time I was sober again the money was 'most all gone.

and

Draft additions 1993

A spree; in Sport, a successful run, a winning streak; esp. in phr. on a tear. U.S. slang.

The quote may be explained as

Foot Locker is proving that expansion isn’t everything. The sneaker chain’s sales per square foot have been rocketing even as the company’s store count shrinks. That’s done wonders for Foot Locker’s profit margins and stock price.

As to your other questions, the answer is that in a tear in that sense is probably not all that common, which is why it's not included in dictionaries. Google Ngrams may be misleading, because a large number of results will be for the lachrymal tear-stained or for a literal tear (=split, rent).

Saying "See you on the field" is fine, because your friend knows you aren't a member of the team and therefore won't actually be ON the field. But when you tell someone you'll "See them there," it's usually understood that you're going to be "there" yourself.

In that context, I'd argue that saying "See you there" is very misleading, and your words could conceivably create confusion or make someone a little angry. But if the person you're talking to KNOWS you won't literally be there, then there's no problem.