Does 3.3v ground and 5v ground connected will affects circuit?
Your micro controller runs at 5V and the WiFi module runs at 3.3V. The RX and TX lines also run at 5V and 3.3V respectively. To use the module in conjunction with the micro controller, you need a level converter which would convert 5V into a 3.3V signal.

To do so, you need to bare in mind that the serial lines (RX,TX) run at reasonably high frequency. For a basic application like this, you can get away with using general purpose transistors. For the circuit below, I have used two NPN transistors BC337.



When a micro controller pin is HIGH, Q1 turns on. Base of Q2 is pulled low, keeping Q2 switched off, therefore, Output is HIGH at 3.3V. Vice versa when micro controller pin is LOW.

This way a 5V signal can be shifted to 3.3V (or any other level). 

Did a search on stack overflow, could not find anything close to this description to avoid any repetition. Hope this helps.