More power output can be bad because of the multi-path reflection and makes it worse because then just higher energy reflections that "look" more like valid good signals. When it comes to quads they do go through a lot of abuse so adding a bit of padded foam or thick double sided tape under things can help absorb some impacts but also I always zip tie my antenna and my battery wires to the frame since if they aren't strapped down they tend to get destroyed in crashes (either things wiggling free from connectors or otherwise getting chopped up by props)
Regarding the different radio links really you have two radio links just to be clear there is the video radio link and then there is the control video link (totally separate). The radio link uses 2.4GHz roughly (usually) and the video uses 5GHz frequency roughly. All the radios use some set of "channels" or ranges of frequencies for sending the signal that is somewhere around 5GHz (or 2.4GHz for control link), believe each channel is about 5-20MHz wide so say 5828MHz - 5848MHz might be considered "one channel".
After years of trials and tribulations in San Francisco apartments, the single best thing I did for my home network was to switch most…
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^^ some good insight and detail in this write up about wifi and 2.4GHz vs 5GHz in that application.
Anyway TLDR I just meant it is good to have matching antenna for a given radio link. So say we are talking about the control link, it is "generally good" to have the same kind of antenna on both the RX and TX of any given link because the resonant frequency of the antenna is what allows it to both transmit and receive, so if two wires used as antenna are exactly the same length then they are effectively 'tuned' to the same frequency at a physical level. I say "generally good" to match because sometimes you want the transmitter to transmit in all directions and a receiver to be more directional or vice versa or may want both sides to use more of a "directional" antenna that basically blocks signal from one side and "sees" more of a signal in a particular direction.
Back to the mutlipath thing I believe polarized antenna (cloverleaf style) typically are good at rejecting some of the bounced signals because the signal is polarized by the antenna and the receiver has the same polarization and anything not aligned to that polarization will be ignored (pretty sure when signals bounce off things the signal polarization changes).
Also regarding your particular issues, it could be running the VTX at higher power output is creating too much heat or has in the past created too much heat on the VTX and so it's malfunctioning at the higher output levels too (or just drawing too much current for whatever is supplying it). Making sure it has an adequate power supply and the power is "filtered" with a capacitor can help with some of those issues but kind of a lot of guess and check (this is where oscilloscopes really come in handy, can get a cheap one that can be somewhat helpful for debugging PWM signals etc. but I eventually decided to get myself a nice fancy sigilent one... cause this is the kind of thing I like to nerd out about)