Re: cables through metal studs
There is not a maximum amount of cables exactly.
There is a maximum number of current carrying conductors you can bundle before you have to derate.
For 14 AWG and 12 AWG NM cables you can have 9 current carrying conductors bundled as long as you want.
Go up to 10 current carrying conductors and the derating will likely be enough to make 14 AWG unusable on a 15 amp breaker and 12 AWG would need to be on a 15 amp breaker.
As always this is not an absolute, temperature and the type of circuit can effect this figure.
Also you can bundle as many as you want for distances of less than 24"
Some will say running sideways through the same holes in studs is not bundling but I have not found inspectors feel the same way.