Li-po cell in RF remote
The simple answer to your first question is yes, there are lots of draw backs to LiPo cells. They are expensive, large, sensitive to temperature, shock, over charge, under charge and subject to various regulations due to their fire/explosion risk. And that's all in storage, charging gets more complicated (temperature, current and voltages all need to be monitored to charge them safely). It is up to you to see how they will effect the end product. If you are just doing a quick one off for yourself, it'll be fine. If you're selling 10 million a year, you'll need to analyse that yourself, or pay someone to do it for you.

As for your second question, you say your processor can take any voltage from 1.8 to 3.8V, and claim your cell is fully charged at 3.5V, empty at 2.9V, so from those numbers why would you use a regulator at all?