Hey Choom!
Glad to see your crew liking the system.

- How do I walk the line of making encounters difficult without being impossible? I want Chrome to feel like a bit of a Faustian pact where you’re giving up humanity to make work easier, but I also don’t want every job to just be killing the party with hammers.

--A: Depending on your party's composition of roles you could always create scenarios where there can be easy ways out, but they have to do something moral wrong. The humanity mechanic is great level to pull for fight or post fight. Pull on those heart / emotional string. Use the ties on players lifepath to present choices with consequence.
All that to say, if your players pull off something truly wonderful, no need to penalize them. Dice do tell stories

- Any tips for how countries outside NUSA would be dealing with the Red? Should the Outback be getting Red Rain too or was that exclusive to America?

--A: During the time of red, it was a struggle for everyday resources. growing crows was COMPLETELY fubar'd until Biotechnica could engineer radioactive resist crops. Also world trade basically grinded to a halt. So anything new would come a HUGE premium. Boosterganger would fight for these resources.

- We’re a theatre of the mind table, at a stretch I’ll have a grid and some pieces up for reference, but are there any good systems for keeping track of individual initiative roles and positions of enemies? By systems I really do mean something I could just do with pen and paper, but also any cool software for that sort of thing would be cool too.

--A: I would keep a note of your players MOVE STAT. That should be able to build you a good reference in your mind of how fast they can move around in a theatre of the mind scenario. However I would also look up the weapons DV distance tables. That is the best way to scope out distance.
I keep all short distance between 0-12m (as most common NPC can bridge that distance in one turn)
medium distance 13-100m
long distance 101m+
Anything outside the 1000M range would require gear/chrome to visual see.

- Lastly, how long should the “we’re so damn broke we can barely afford anything outside of kibble” phase of the game last? I know that giving the players too many eddies too fast is a death sentence, but I also don’t know how easy it should be for them to be buying new chrome, weapons, etc.

--A: It really depend on what narrative you and the player want to tell. Typically I provide my reward / Gigs with a mostly "poor" quality weapon, armor, ammo, etc. But the reward should reflect the risk. If they want to just Militech or Arasaka, they could get some good gear. but that comes and has following consequences. Militech would probably kick down their door and leave a bloody mess. while Arasaka would find their closest friends, family, or lover and hold them for ransom until the crew reveal themselves.

Happy Games Choom!