If I reset my network settings on my iphone 5 on iOS 6.1.2, will it update to 6.1.3?

I have a jailbroken iphone 5 from sprint IOS version 6.1.2, I unlocked the phone using a chip called rsim7+ to be able to use on any carrier and the internet 3g worked great, but one of my friends changed some of the network settings and now the websites do not load, and I do not know what the configurations were. So my question is, will going to settings, and resetting the network settings change the network settings to the way they were originally before, WITHOUT updating to 6.1.3? Or will restoring the network settings automatically update my phone to 6.1.3? I need to know this because I cannot update since there is no jailbreak for iOS 6.1.3, and my phone will not be able to be unlocked on that version. Thanks!

Added (1). Thanks! One more thing does master resetting the phone (erase all content and settings) update to 6.1.3, or still stays on the same iOS?

Nope.

No, it will not update to recent firmware, until you tell it to do so. Go ahead and reset the network settings wont disturb your jailbreak.