re: "Does Upwork live chat support closed?"
Live chat support is not available to all users at all times. Don't worry about that. If you have a question, just post your question here.
re: "It's better to use Upwork communication system to contact the client. If your client asks you to talk outside of Upwork you may agree but don't work outside of upwork."
I think the wording of your post potentially could confuse people.
Before you have been hired officially with an Upwork contract, a freelancer can not work on the project. Because the freelancer will NOT GET PAID.
In order to get paid, a freelancer must be OFFICIALLY HIRED with an Upwork contract.
A freelancer must not communicate using an outside tool.
If a client asks you to talk outside of Upwork, then you need to decline. You need to have them either (a) talk to you using the Upwork Messages tool, or (b) have them officially hire you.
If a freelancer is caught communicating outside of the platform before a contract is in place, then the freelancer can be suspended or otherwise penalized.
Also: The client is probably a scammer - not a real client - if he asks you to communicate off-platform and won't agree to talk to you on the platform when you explain the rules.
I have utilized the video conferencing feature available through UpWork on several occasions with an international client. Even though I have an established relationship with this client now, going through UpWork keeps things simple and gives me a bit of reassurance.
If using Zoom (outside of UpWork) makes you feel uncomfortable or uneasy, perhaps you can ask your client why he or she prefers Zoom. Is it to record your conversations? While it can feel awkward or uncomfortable bringing this up with a client, open communication is important to successful professional relationships. I'm not trying to tell you what to do, but trust your gut and don't feel pressured to do something (when there is a safer and available option) because a client wants you to.
Best of luck!