Can you buy apps on another iTunes account?

I'm wanting to log out of my current iTunes account on my iPhone, log into another to buy/download a few apps/albums and then log back into the first iTunes account.

Will this:
A) Delete the apps/albums I've downloaded?
B) Make the apps/albums show up on all devices linked to the original account even though bought/downloaded on the second?

I'm wanting to do this because I'm currently logged into a shared family account but do not want them to get charged so I want to log into my own account so apple charges me and not the family.

Do it on a computer.

Yes it's possible but it's only safe when your using a device other than Apple because this way you be able to create an apple account safely as the system won't be able to track your already existing Apple ID which can be easily tracked when you are using an Apple Device. Hope that helps