Do I have to restart my computer or applications after I receive a new micropatch?

Absolutely not. Not having to even restart the vulnerable application (much less the entire computer) is one of the main benefits of micropatching.

When a new micropatch is received by your 0patch Agent for a vulnerable application you have installed, it will immediately get applied to this application in case it's running - and you won't have to do anything, or even notice anything unless you have your 0patch Agent popups configured to inform you of all events.

In case the vulnerable application is not running, the micropatch will get applied to it every time it gets launched.