Hi, 1C means 1 time the capacity of the battery.
If the battery is a 500mAh 1C means 500mA of max charge/discharge current, if it is a 1000mAh then 1C means 1000mA/1A discharge/charge current, and not 1 Coulomb.
There are batteries that will have much higher discarge capability, like 20C, if you have a 500mAh battery rated for 20C you can safely pull 20x 500mA of current without causing cell degradation.
Given the low power nature of your system a GOOD LDO is the way to go, but bear in mind that a LiPo discharged to 2.8V is dead and should be scrapped because charging it may cause the battery to explode.
I would put the cut-off at around 3.1v and just run the whole system from a 3.0v LDO, also keep in mind that LDO's dont like ceramic caps for decoupling, either use a ceramic with a low ohm resistor to emulate a tantalum, or use a tantalum cap at the input and ouput pins of the LDO, or it can/will oscillate.
A DC/DC regulator for low power usually doesn't make sense, higher quiescent and given the low loads and very low difference in voltages the duty-cycle will be also pretty low leading to more losses.
DC/DC emit RF noise, but it can be tamed down or we wouldn't have cellphones today.
Take a look on this TI part numbers:
http://www.ti.com/product/LM2936http://www.ti.com/product/tps780/descriptionBoth are low quiescent LDO's that are made for battery operation, on of them is made to use ceramic caps and both have 3v versions.
And LDO's will be always lossy, they are linear regulators, so they will turn the extra energy into heat, but a buck in this situation will do the same due to such small conversion, and its a wide range(3 to 4.2v input into a fix 3v output).
For low current battery level measurement the 10M resistor might turn into a noise generator and nothing much, the usual ADC input impedance is around 10Kohms, if you want to sample from a cap, use a 100nF cap, you already have some on the board for decoupling, so its one less part to stock, but you might need to drop those resistors a lot, I had zero luck using 1M with Atmega, the ADC load causes the values to drop to near zero even with a cap.
Also, study the PTC datasheet, a PTC is a resistor, its resistor goes up as more current passes through, but it is a relatively slow method, so you battery will happily dump a couple or more Amps in case of a short, a 150-200mA PTC might be better.