How to choose the appropiate analog power supply filter inductor
1) The inductors are used to filter noise from supply voltage. As each supply node has its own inductor, noise caused by periodic gulping of current on one supply node cannot pass on to other supply nodes and cause problems taking the sensitive measurements.

2) That is a good question and there may not be an answer. It seems that the evaluation kit for the pulseoximeter chip used a 10uH inductor LPS3010-103MLB everywhere, most likely to reduce cost by using same part for everything, and that reference design got copied everywhere. So as long as the parameters are reasonably same almost any inductor could be used.