Android build questions

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