1/4 WL Strip Antenna Questions
Welcome to the antenna/RF world -- also known as the land of black magic! I'll try to answer your questions:

There must be an error in your JLCPCB microstrip calculation -- and did you mean 11.55 mil (thousandths of an inch) or 11.55 mm? The typical 50 ohm microstrip, on 1.6mm FR4 board, is about a 2.65mm wide trace, with continuous ground plane underneath. Obviously the IC pad is smaller, and it's ok to use narrower traces for short distances as you connect the SMD components, but as soon as possible, do a smooth taper up to the 2.65mm width.

Several factors combine to make a PCB trace antenna resonant length shorter than the free space quarter wavelength. First, the PCB dielectric slows the propagation of the waves along the antenna. Second, antennas exhibit an &quot;end effect&quot; which causes them to resonate at a lower frequency than the theoretical quarter-wave (for monopoles) or half-wave (for dipoles). Someone at Nordic has experimented and come up with the recommended length. Unless you have a vector network analyzer and want to invest time experimenting, I'd just duplicate their design.

That &quot;hook&quot; shape is just one of many possible designs, all of which have to  satisfy several competing demands: low SWR (i.e resonant), 50 ohm impedance, bandwidth across the needed spectrum, efficiency, and if possible a radiation pattern without big nulls (holes) in it. Again, without expensive equipment, like an anechoic antenna test chamber, you're unlikely to stumble on a design better than Nordic's.


However I do not want to discourage you experimenting. You won't hurt yourself, and you may end up pursuing a hobby or career involving antennas. I spent my first 5 years in EE doing just that and it was a blast.