Can one use a diminutive w/ a patronymic in Russian?

no

friends can call each other that way jokingly (esp. Alksandr Aleksandrovich would be often called San Sanych etc) but not officially

and Vlad is not nickname for Vladimir

Trollface is either exactly what it says on the tin or an extremely confused person. First name and patronymic is the opposite of a familiar form of speaking. And no, you can't use a diminutive with a patronymic, it just sounds incorrect. Like saying "I don't seem to can" instead of "to be able to".

No, it is NOT accepted in Russian language.

Diminutive+patronymic can be used only for joke and VERY rare.

Also Vlad is diminutive for Vladislav, NOT for Vladimir.

Diminutive for Vladimir is Vova.

Yes, that's a very common way of referring to people. However, you would never talk to the prime minister in such a manner; calling someone by his/her first and patronymic names is considered a very familiar form of speaking and would only be reserved for friends, family, and other people who are well known to you.