I have a single entry non-immigration o visa from Savannakhet for the reason of "being father to a thai citizen". I have around 3 weeks left on my stay and i'll soon head to Phibun mangsahan to make a 60 day extension.

What i'm curious about if this is the correct papers i need with me:

My child, her thai passport and copies of passport.

Original tabien baan and copies of it.

Original birth certificate and copies.

My passport, copies of my passport as well as copies of the visa, latest entry stamp and TM6 form that's stapled in the passport.

Also:

Do i need any papers of the mother of the child?

Any issues that my passport will expire end of September 2015 although the extension of 60 days will end around 20-23 August?

You child passport will not needed nor copies.

You should not need anything from child's mother but having a copy of her house book and ID card would be good to have if asked for.

As long as your passport is valid for the length of the extension your passport expiration date will not matter. But you need to get it renewed soon. At this time you will not be able to enter any neighboring country with it since they require 6 months of validity.