3.3 V LDO voltage regulator for microcontroller (STM32F103x)
The question about quiescent current looks legit, so I'll answer that. Yes, your circuit should accommodate for quiescent current which can be as high as 10mA in the worst case. If you don't, you can't rely on output voltage anymore.

Clearly LD1086 is not a good choice to power the microcontroller from. It is designed to provide high current (up to 1.5A) which you don't need, and has this minimum current limitation which matters to you. You can probably get away with a much smaller and cheaper regulator, something like a NCV663.