M4R5_FPV

From what I heard so far is that they fixed the 04x pro but wont fix the 04o pro but instead release a new one.. how accurate this statement is is questionable but most likely true. There is a firmware update on their website for the latency issue but only for 04x pro as mentioned.  I do own the 04o pro and as a casual freestyle pilot i dont mind it at all. Only if you very sensible to latency it will matter. 
Btw I wrote skyzone a few days ago because i curious, still waiting for an answer :) 

Make sure that the transmitter is powered "off" before connecting the usb cable and then power it on. 
Use a cable which can transfer data and not a "power only" cable. 

Download the "ComPort Driver" if needed...
https://www.st.com/en/development-tools/stsw-stm32102.html

Check motor direction and order on the motor tab in betaflight.

Is the omni a TrueRC Sigularity antenna? As those are great! the Realaac triple feed patch are also nice especially since they are quite cheap. I own pretty much the same set up for my analog system (well i own skyzone goggles) and never got disappointed. 

@fensShadow grass and dirt as well as residual solder flux can lead to corrosion and also potential shorts as those can be conductive. So its best practice to clean it regularly from dirt/grass as well as after soldering to get rid of the residual solder flux and therefore prevent bad things from happening ;) Isopropyl (IPA) works great and evaporates residue quickly afterwards. Use at least 90% or better 99% isopropyl for it ;) again great work on the first solder joints!

The save way is to replace it

Did you check in betaflight if the sensor is set up correctly? You can recalibrate it if necessary. Otherwise it will fly fine. The risk is that you could damage your lipos as it won't trigger any warnings this way. So it could be a fried voltage regulator or just a betaflight mismatched setup. I would check betaflight first. Than if you got a multimeter check if any of the regulators is dead. Btw dirt on the board could create a short.

I don't have either but if you place for the Vtx on top of the FC (because of its short cable) and print a different mount (cam is 14x14mm) as far as I know it should work fine

I absolutely agree that for the most pilots its pretty much useless but to some extend it can be useful to showcase flight time with different prop pitches or sweet spot for a certain frame size. Which prop size or pitch would be better if someone wants to fly doing cinematic shots compared to someone who wants to fly freestyle or someone who is a racer. Of course a lot of data goes into it as you mentioned. So it would be more a theoretical tool than a "real world" calculator. 
No worries It was just an idea 😜 I thought of it like the FPV goggles comparison tool.

if you just want to power it from the fc and not use the remote control function i would choose the JST cable. 
Just remove the yellow cable as this is the PWM cable to remote control the camera. Instead you can set it up through the app to record as soon as you plug in a lipo. 
The red wire goes to any 5v and the black to GND. 
For mounting it you will either need find someone who can print a mount for you or If you got a 3d printer  print one yourself. there are mounts available on thingyverse, printables etc..  e.g. https://www.thingiverse.com/thing:6613414

Hmmm... Desync, ESC failure, prop failure,.. there are a few possibilities.. but I don't think you hit a bird... overall it's just sad to see it falling!

do you mean something like this? interesting project for sure!!

Well it can have multiple reasons why it is doing that. Loose screws, cracked/broken frame, PID and filter tuning, wrong motor order, wrong motor direction, wrong fc direction,...) 
Can you post a screenshot of your PIDs and filters in Betaflight so we can rule out a simple tuning issue (a too aggressive tune). 

LOL

The brand matters mostly because you can find a lot of "fake" 18650 batteries with high MAH numbers. Brands which offer great ones are Samsung (35E), Panasonic/Sanyo (NCR18650GA), Molicel (M35A or P28A/P26A), LG, Murata/Sony... around 3200-3500mah above that i wouldn't trust them.
You could also buy directly Radiomaster's 18650 with 3200mah.

well i m sorry to say it but I see an issue. The Emax eco 2 2004 motors use a T-mount (1.5mm) for the prop and the props you ordered need a 5mm hub. Also the pitch of the props would need to be lower otherwise it will stress the motors quite a bit.
while the motors can work with a 5" frame on 4s it will not have much torque and if pushed will run hot very fast. it will be more like a cruiser (maybe long range) but definitely borderline for freestyle. 
Standard motor sizes for a 5 inch drone are 2207 or something like 2306..

the rest looks fine.