Looks like you're off to a great start!
I don't want her to be a combat bunny, but I do want her to not be a complete liability when that happens!
You've got 14 dice with your claws, and since you have a pair that gives you a point of reach (which cancels out a dodge die). I'd say for a non-combat specialist, you're good. You won't be one shotting any bad guys, but you didn't plan for that going in. Do be aware that the 5P damage value is pretty light.. while you can handle the odd guard by your lonesome you can't handle them
quickly. Bear that in mind.
I do want the character to be able to negotiate (etc) in Japanese as well as English - what level do I need for that? She currently only has Japanese 4 (with a speciality in Speech).
Languages are the bane of faces. Presumably your native language will be English (that's not reflected in the chummer stats you posted). For any non-native languages, your Social limit is ignored and you use the number of ranks in that language instead as the limit. So Japanese 4 means you have a limit of 4 when using social skills in Japanese... You might consider either making Japanese her native language, or if you like the idea of playing a gaijin you might want to look into the Bilingual quality, allowing you to have both English and Japanese both as native languages.
I do have spare cash to spend on random extras that one needs as a Runner - just not got them yet. If there are significant things I need to buy, I am happy to drop a level of Muscle Replacement (to take me to Str3, Agl5).
You probably can't afford to strip out the point of muscle replacement because your damage would drop even lower, and your Physical limit is already borderline unacceptably low.. going to 4 would be awful for a sneak specialist.
But some things you'll likely need:
A fake SIN.
You still need to buy a commlink (the implanted cyberware doesn't include a commlink; it's just a "port" to put it in inside your body)
Vision and Hearing enhancements. (contacts/glasses, earbuds, with various enhancements.)
DNI- either a datajack or trodes (if you're using image/sound link)
AR gloves (if you're not using DNI)
Since you want to be an infiltrator, you'll want to address being able to get into places you can't just sneak into. That's either contortionism or picking locks. You can throw some mix of essence, nuyen, and/or skill points to achieve these. With skills being your A priority, I'd recommend finding skill points for Escape Artist, Locksmithing, and at least a couple points in Hardware. Depending on the money you have available, you can also/instead consider the various tools like maglock passkeys and sequencers. You're pretty low on essence, but there's some fun cyberware out there that is immense help for squeezing through tight openings.
I'd also recommend buying some sensor tags. You're the infiltrator; who else is going to plant cameras around inside the place you're casing?