If my phone is in sleep mode will it still ring? If it rings in sleep mode, will I have to go through the process to unlock it before answering the call?
The simple answer first
Yes, the phone will ring in sleep mode.
No you do not have to go through the unlock process to answer the call.
Make sure that you have the phone set to keep WiFi on during Sleep
Settings -> WiFi -> Advanced -> Keep Wi-Fi ON during sleep -> Always
For the not so simple aspect of the answer, please review this discussion
Is your phone losing its WiFi connection while sleeping?