I know the major components of rectenna should be
- Receiving antenna - Patch Antenna
It needs to be an antenna. Not necessarily a patch antenna.
- Matching circuit
- Low pass filter
- Rectifier - Schottky diode
The Low Pass Filter needs to come after the diode! Otherwise, there'd be no more signal energy to rectify.
For number 1(Rx): I have found some information saying that the gain wouldn't be important for Rx
That information is very misleading, probably even wrong. The effective area of your antenna defines how much power you'll be able to extract from the electromagnetic field.
What you'd want is an antenna with a high effective area. That usually comes with high gain.
For number 3(LPF): I have found another article on https://www.researchgate.net/publication/266872359_Designing_Microstrip_Low_Pass_Filter_In_ISM_Band_For_Rectenna_System that connects the LPF with patch antenna by using microstrip. My idea of LPF was by using RC or LC and when I see that my mind was blown away lol. According to the complex calculation on the article, I am not sure can I follow that?
You're using microwave frequencies. Your Ls and Cs don't look like components there, anymore. You need to use microstrip lines (and other types of waveguides) to even just transport the signal – a cable won't do.
If you understand none of the equations there, that's pretty normal, but that also means that you won't be designing an efficient rectenna soon.
For number 2: Apparently almost every component will have its resistance so how can I calculate the optimum matching circuit?
Sorry, that is far too broad. If you really want to use a patch antenna, then the matching of the patch to the microstrip line is done by calculating/simulating the optimum recessed feed inlet length.
Then you'd need to somehow match the diode to the microstrip line, which is mathematically impossible (the diode being very nonlinear), but you can get "good enough" for ranges of amplitude that you care about.
Finally, you'd need to have a sink for the high-frequency content that the diode produced, (the low pass filter + termination) to avoid that getting re-emitted by your antenna.
These are three pretty hard problems, and it'll probably take someone with a lot of experience and equipment quite a while to figure out a satisfying way.
I have to create a chart that has all the voltage i/o, current i/o, gain i/o, power i/o for all the components, how am I able to calculate those for antenna, matching circuit, LPF and diode? It looks like impossible to me now..
I'm sorry, I think it is impossible for you right now. You probably need a lot of Electrical Engineering basics, and then very specific knowledge of working with nonlinear RF elements.