If you go online but then switch to another app before accepting a rider's trip request, a pop-up notification may display every 3 minutes to remind you to go offline if you don't wish to receive requests. When you're on a trip, your app won't send these pop-ups.
Your Uber driver app continues to run when you're using other apps or the phone. GPS info is continually collected to ensure your trips are recorded for accurate fares.
Follow local regulations regarding phone use. Please be mindful that talking on the phone while driving can be distracting and dangerous. Some riders also find this rude and unsafe.