Why does 中 come first in order when it is in the middle (i.e.: 中小、中前)?
For 中小学
It is a common practice in Chinese to put bigger things in front of smaller things.

In address, 北京市朝阳区, where 朝阳 is a part of 北京-
In dates: 壬申年正月初七日 or 一九九二年二月十日
In people: 全家老小 where 老 elders are in front of 小 children. 公司上下，where 上 means the executives and 下 means workers.
And here in schools: 大中小学

But the rule is not always true when 1, the number of items is small 2, you want to emphasize some of the items. For example, 中杯，大杯，超大杯, where the 超大杯 is extraordinary.
For 中前期
I want to say, it is a rather vague phrase to me. It can mean either 中期 and 前期 or the early part of 中期, which are different. These abbreviations often appear in time or location descriptions but are not recommended. You should either say 中期和前期 or 中期的前半 to reduce the confusion.