Putting 了 in both parts of separable verbs: is it mandatory? My sentence is


  我们八点已经开始上了课。


Can I put 了 at the end of sentence? Or is it mandatory to put between both parts of 上课 (a separable verb)?
开始上了课 is not grammatical. 开始 means 'started', 上了课 means 'have finished class', You cannot "Started to have finished class"

A  grammatical sentence should be 我早上上课 (I attend classes in the morning) --> 我早上上了课 (I have attended classes in the morning)

And yes, you can insert 了 between the verb and noun in any separable verb to indicate it is completed action

Example:

看書 (read book) --> 看了書 (have read book)

吃飯 (eat meal) --> 吃了飯 (have eaten meal)

逃學 (skip classes) --> 逃了學 (have skipped classes)