unless you do something the government requires a lisence, I think you can do most things without special permission.
Example 1: Buxiban should register its employees to the government, but it is not your responsibility and you don’t need to get an approval.
Example 2: no need of permission. University most probably request you to give them estimate and bill, and receipt.
If your monthly sales is more than 40k NTD, you should register yourself as a business entity at taxation office, and they require you to issue receipt.
Articles 28~31 of Value-added and Non-value-added Business Tax Act
Regulations Governing Taxation Registration
Apply for Taxation Registration
I think editing isn’t included in gaofei, unless your name is put on the published documents. Maybe science writing by your name is.