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2) I have radios that have a receive rating of -83dB. I have done the link calculations and get a -47dB. This calculation is done with a 50mW transmitter going into a 500mW amp and a 9dB omni.

3) I get similar calculations with a 100mW transmitter going into a 500mW amp.

Just to clarify: is the 500 mW amplifier a fixed 500 mW of gain, or is it variable gain, pulling any input signal up to 500 mW total output power? I ask because you said your output power from the amp was 27 dBm, which equals 500 mW. If the amp was a fixed 500 mW of gain, then the output power from the amp would have to be greater than 500 mW.

If the amplifier is a variable gain amplifier, then the transmit power of the radio doesn't really matter much, especially if you don't have very much cable loss. If the radio is at 50 mW output power, the amp will add 450 mW and bump it to 500 mW total; if the radio is at 100 mW output power, the amp will only have to add 100 mW to get to 500 mW total. In the second case, the signal-to-noise ratio will be somewhat better, but this will probably have negligible effect on this particular link. SNR is a much bigger deal at the receive side, where the signal is very weak relative to the noise, than it is at the transmit side, where there is typically plenty of SNR to spare.

I didn't verify that the FSPL was right, but assuming it is, you've done your math correctly. Keep in mind that, because you have an amplifier in the system, you will have to do TWO link budget calculations--one with the amplifier and one without. The reason is that, unless the amplifier is bidirectional (which I assume it isn't, or you would have mentioned it), the signal going "outbound" will be amplified, but the signal coming "inbound" won't. This leads to the Unbalanced Power Effect that I described earlier. Dual link budget calculations may reveal that the un-amplified side doesn't have enough signal strength to make the link viable or to achieve the data rates that you require.

As a rule of thumb, I try to avoid using amplifiers. I try to get the signal strength that I need through higher-gain antennas, higher output power from the radio, and better receive sensitivity in the radio. Higher-gain antennas avoid the Unbalanced Power Effect because they work both in transmit and receive. Different output power and receive sensitivity can create the UPE, but in a point-to-point or point-to-multipoint bridging scenario, the radios at either end of the link are usually the same, so they will have the same output power and receive sensitivity.

If using amplifiers is unavoidable, I buy the highest-quality amplifiers I can find and I make sure that an amplifier is placed at both ends of the link.

I had a case once where I was using an amplifier with a variable transmit gain that output a fixed 500 mW and a fixed 12 dB of receive gain. I was using them with 8 dB omni antennas. This system was designed to work at distances of about two miles, if I remember correctly, but in the lab, the antennas were only a few hundred feet apart. The RSSI at the receiving radio was about -40 dBm, but the link was terrible. Pings wouldn't go through. We removed the amplifiers and everything was fine.

We wired the radios directly into each other using a short run of coaxial cable with a variable resistor inbetween them, then we measured the throughput and number of corrupted packets seen at different RSSI values. We found that the maximum throughput was achieved at RSSI values of about -60 dBm. Above -60 dBm, the number of corrupted packets increased significantly, maxing out around -40 dBm. Below -60 dBm, corrupted packets decreased, but so did throughput, because the signal strength and SNR was not sufficient to maintain higher data rates.

This radio was technically rated to overdrive at -10 dBm, but our test results showed that overdriving the radio is not an all-or-nothing thing. As the RSSI approaches the overdrive threshold, corruption increases.

In 802.11, it's common to think that more power = better, but in reality, too much power can be as bad as too little. I think that there is a "sweet spot" for RSSI between about -60 and -80 dBm. I try to design point-to-point links so that the RSSI at the other end falls into this sweet spot. It might be tempting to add an amplifier and push the RSSI up to -40 or -50 dBm, but I think that this temptation should be avoided.