How to Increase RF Amplifier Efficiency?
I am not an expert on the subject of power amplifiers, but since there hasn't been an answer, here's my attempt:


Defined "good."  A straight-forward, inexpensive way would be to measure the output RF with a power meter (directly attached, no antennae) and divide it by the circuit's power consumption.  Obviously, that's a full-system efficiency and not specifically the power amplifier.
Not especially.  Amplifier linearity and power efficiency are inversely proportional.  Using a less linear amplifier will be more power efficient, but distorts the signal reducing your SNR and link margin.  The theoretical efficiency for a class A amplifier is 50%; in practice, much lower.  That isn't to imply this is a "good" amplifier and better options don't exist.  Make sure any required output impedance matching is properly designed and populated.

In the case of BPSK (or QPSK) you can sacrifice linearity for power gain as the phase of the signal contains the data and not the amplitude.  Since you are using BPSK modulation you can safely consider other classes of amplifiers like AB, C, D, etc.

There are a couple of work arounds:

In mobile technologies, you have things like offset-QPSK and &pi;/4-QPSK to reduce the dynamic range required, allowing a less linear power amplifier.
Techniques like pre-distortion are used to correct for amplifier non-linearity, allowing use of less linear amplifiers.

Don't use a larger amplifier than you need.  Operating a 10W amplifier at 1W may be considerably less efficient than operating closer to 10W.  This is a side effect of the bias current in class A amplifiers.