1) i/p refers to power at input, o/p power at output. For down-conversion i/p at RF port, o/p at IF port. For up-conversion i/p at IF port, o/p at RF port. The difference between i/p and o/p is called conversion loss or gain; depending on mixer technology. LO is always an input signal, but it should not vary (i.e. power level should be kept constant); that is to say the LO is only use to translate the IF into RF (for up-conversion), or RF into IF (for down-conversion).
2) 1dB compression - look up this term for amplifiers. It is the point at which the gain deviates by 1dB from the expected gain. That is to say, the gain should be constant at low input power levels; gain at -40dBm input level should be the same as gain at -39dBm, -38dBm, etc. Keep increasing the input signal level until the measure gain decreases by 1dB. That input level is the input 1dB compression point, that output level is the output 1dB compression point. For linear systems you want to operate below this level (considerably lower) to avoid distortion.
3) As for IIP3 or 3rd order input intercept point, it is a measure of non-linearity. Add two tones at the input of a non-linear device at a power which is significantly lower than the 1dB compression point. Measure the unwanted tones at the output and compare their levels to the wanted tones at the same output. Suggest you read Introduction to Radio Frequency Design by Wes Hayward, or RF Design Guide from Pete Vizmuller.