i don’t know what are you looking for so i’m just gonna drop some resources that i’ve used:

starter: https://www.antenna-theory.com/antennas/main.php

more comprehensive: https://www.microwaves101.com/encyclopedias

and on top of that, various amateur radio pages, some are indexed in dxzone.com

there seem to be two hard limits on antennas in general. one is for approx lossless antennas that are large compared to wavelength: gain, beamwidth and size are related through diffractive limit https://en.wikipedia.org/wiki/Diffraction-limited_system it’s really about capture area, which is intuitive for things like parabolic reflectors, but for things like yagi antennas there’s some defined capture area that ultimately depends on their length

the other one is on non-directional antennas that are small compared to wavelength. basically one good antenna that you can make is halfwave dipole, you can try various trickery to make it smaller, but this comes at a cost of either smaller bandwidth or increased losses, or both to lesser degree. it might make sense to make an antenna with 70% efficiency which is 3x smaller for example. it all depends on precise requirements

at the end of the day the most important material in any antenna are tradeoffs

if you want to measure anything rf, you’ll need a vector network analyzer like nanoVNA (some $40), this will be very useful in tuning/matching antennas (and making sure you won’t get reflections that could potentially damage transmitter if you screw up badly enough)

antenna design is usually limited by one of these things: size, gain/radiation pattern, efficiency, bandwidth (fixed here, entire 2.4ghz band)

you can probably use off the shelf antennas used for drones if these are small enough for your application

soldering coax can be tricky, don’t melt center insulation. you’ll need to size microstrip line so that it’ll have impedance 50 ohms as well https://www.pasternack.com/t-calculator-microstrip.aspx

1. no, this is fine, you can find it in routers all the time (usually with printed antennas, or wire antennas)
2. so it seems, however remember that at microwave frequencies you might start seeing distributed elements as a part of matching circuit (patches, open or shorted transmission lines etc) every fraction of mm is critical. i don’t know what impedance gets this thing on output, but it might be very well non-real. it’s usually done so that everything is matched to 50 ohms
3. assuming that output is matched to 50 ohm, which is usually the case, you can use any length of coax, as long as losses don’t kick in too badly. this means you also have to make your antenna 50 ohms. i see you’re using ceramic antenna, which provides matching circuit for you, but there are other options like inverted-F antenna (3cm long) or even smaller zigzagged *inverted F antenna or halo antennas (some 2cm dia), which would require matching. tradeoff is better efficiency (less heating; one of these antennas wastes almost 40% of power) and the fact that you can make them on your own

2

this only works well if you have good soldermask in place