Hi Chakri,
1. I didn't try that one out. But maybe it's solved with this one https://nginx.org/en/docs/http/ngx_http_proxy_module.html#proxy_ssl_session_reuse as you might need to forward the handshake then.
2. Yes, you can do that - see my example here https://github.com/judif/mtls-nginx-nodejs-example/blob/main/node-server/server.js#L33
3. Not sure if that works out with the question 2 above. From what I've experienced it is not possible to forward the client certificate, so I introduced header parameter forwarding the certificate information https://github.com/judif/mtls-nginx-nodejs-example/blob/main/nginx-server/proxy.conf#L30
Hope that answers your questions? Let me know if you have any doubts.