Android build questions

Dear community!
Please write whether it is possible to take such or a similar device and make your own OS assembly for it, for example, register your market, password protect the settings, and so on.
Suppose I want to equip the employees of the company with tablets to perform special functions, while I want them to have my set of pre-installed software, when I try to download something, they end up in a repository organized by me, to protect the tablets from the "fool".
If I understand Android open OS correctly and should it be possible to do this? Or am I still wrong?
Have you worked with cheap Chinese tablets for $ 70-200, what can you say about them?