I will try to answer on some of your questions:
1. What value of inductance I should use with power choke inductor, refer to application circuit?
The inductor value should give you a reactance of several hundreds ohms (at least 300 ohms) in your lowest frequency of operation. remember that as the frequency increases, XL increases as well.
In addition, you should choose the inductor such that its SRF (Self-Resonance Frequency) would be at least twice higher than your maximal frequency of operation in order to avoid a capacitive reactance.
How I define output M.N.? refer to application circuit?
Usually for LNA, you define the output matching network as one for conjugate match. This is because the input matching for noise figure degrades the return loss at the input and reduces the overall gain (mismatch), and as a result you loose power.
If I do a simple output conjugate matching, should I turn on LNA, if yes, is power choke a part of matching network?
You should design the output matching only after your input mtaching network is fully designed and connected to the LNA, because the input matching network will affect your S22. The reason for that is that the amplifier is not unilaterlal, i.e. there is a certain feedback from the output to the input S12.
The choke (power inductor as you named it) if properly chosen, should slightly influcnece on the output mathcing network. Actually, it isolates between the supply voltage to the matching network. Usually from RF signal point of view, it only slightly increases the gain.
So your output matching newtok should be designed to the conjugate of the modified S22 (With the influence of the input matching network).
You should turn on the LNA, in order to measure the output power.
In general, when designing matching networks, pay attention to the stability of the amplifier.
It is very important to check that your required reflection coefficients are located within the stable region.
You can perform stability simulation or calculate K (Rollet's Factor). For unconditional stability K>1