Sure, you can do that. It's called tie lines ...

I just learned a new term. Tie Lines.

What would I need ?
Would my signal chain go like this ?
Mixer XLR in ---> TRS 1/4 Patchbay and then out the back of the patchbay and to the wall jacks.

maestro7879 wrote: 4 pairs in each cable.

How are these pairs arranged ?
4 twisted pairs with one sheild.
or
does each pair have an individual sheild ?

Some may disagree but dual sex tie lines with an XL male and female at EACH end can be very useful. Then add some adapter leads and you can usually get most things patched.

4 twisted pairs with a shield on each.

I don't think that mic and headphones or line level in the same cable at the same time is a wise idea.

You will probably be ok with all mics.
All line level will be fine.

Would my signal chain go like this ?
Mixer XLR in ---> TRS 1/4 Patchbay and then out the back of the patchbay and to the wall jacks.

yeah well try and avoid too many contact points you know... if you want purity....Actually shortest leads are the best outrightly....
Can you just terminate the cable directly to mixer XLR in..that would be best if you can avoid the patchbay there..

.....oh ,, and having a shield on headphone output cable may stress the output stage of the headphone amp ( if it's small )because of the reverse capacitance being greater than two straight cores without shield....... blah blah blah ..... :D

Would this work ?

Would it be possible to just run a small headphone amp on each wall jack thereby eleminating any powered headphone signal going through any of the cables ?

I would still run two mic lines , one line in , one headphone out but the headphone out would no longer be powered until the end of the chain.

Technically possible but you may be over complicating things.
The may still be an issue with Line level mixed in with Mic level. This cable was twisted pairs with 1 overall sheild.
However the multiple HP amps does make for other options later.