Why is there an inductor in this power supply circuit for SAM3X MCU?
1 - The two 10 uH inductors are RF chokes which keep external noise picked up on the UTMI+ interface (such as USB cables) from getting back into the ADC and causing noise.

2 - Yes, those are all electrolytics, presumably tantalums.

3 - The symbols are indeed resistors, 1R stands for 1 ohm. A common convention for resistors is to use XRXX to indicate X.XX ohms, XkXX for X.XX kohms, XMXX for X.XX Mohms, etc.