Gain vs ADC performance vs ADC settling time
"How can i read ADC values more accurate AND faster?" You can not. They are inversely correlated in delta-sigma ADCs. Read how a delta-sigma ADC works here

But you can take some measures to improve SNR characteristic of your circuit by:
1- Following the design guidelines in your ADC data sheet, in particular Grounding and Layout section.
2- Add appropriate filtering in your input stage.
3- Some general guidelines, like using linear power supplies rather than switching if possible, having separate analog and digital ground planes on your PCB, etc.