Pardon me for having many questions.
Please give some comments/suggestions to enlighten me.
1) In the RF circulator datasheet, I saw "forward power and reverse power", can anyone explain what is that about?
2) what are the things that need to know when using circulator?
3) Does a circulator require 50ohm matching for all ports? In what way we can achieve 50ohms? what will happen if I did not achieve 50ohms?
4) signal flowing from Port 1 will flow to Port 2, and signal from Port 2 will flow to Port 3. Does the signal from port 3 will flow to Port 1? By right based on board design, signal shouldn't flow from port 3 to port 1.
You are asking the wrong questions and perhaps don't understand the use of a circulator.
1) The signal flow is indicated by the arrows.
2) You want your TX signal to go to the antenna, and the received antenna signal to the RX. That is the left option in your picture.
3) If your antenna is not well matched, some of the TX signal is reflected inside the antenna and now goes to the RX. If that is your problem, you need a better antenna match. That is specific to the antenna, there is no simple 1 minute rule how to do that.
Just some comment in addition to volker@muehlhaus. volker@muehlhaus is right, if your port to antenna is not perfectly matched, there will be reflection. The reflection will routed to RX port. If your signal is of narrow band, usually it is not difficult to design the impedance matching network.
Another device you may consider to use is directional coupler.
Yes, circulator is better for TX/RX antenna multiplexing. But if you could accept the loss, directional coupler is ok as well. Directional coupler is much cheaper and easier to get than circulator.
Generally the goal of impedance matching is to transfer the greatest amount of power(W=V* A). Suppose your incoming signal is high V, low A. This implies high impedance. Then suppose your next stage wants a signal which is low V, high A. This implies low impedance. To maximize power transfer, an impedance matching network is installed. Often it consists of a transformer, or combination of inductors and capacitors.
For instance, at one time public address systems had a 70V output (at weak Amperes). It could be called high impedance.
The audio signal was wired to several speakers. Audio speakers are commonly 8 ohms (low impedance). A signal of 1 or 2 volts is needed to drive it loud enough so a roomful of people can hear it.
Each speaker-box had a 70V transformer inside, which stepped down the voltage (thus stepping up the current). Thus the system matched a high impedance in the PA amplifer, to low impedance in the speaker boxes.