Yes, we can still use 1.0 agents but, since Zabbix 4.0, the oldest agent we can use is 1.4.
Yes, in a major version, we can mix server and frontend even if they have minor upgrades. Agents are backward compatible till 1.4; however, we'll lose some functionality so it's best to upgrade agents when you can.
Proxies will still work and send data to the Zabbix server; however, they can't receive updates from the Zabbix server. Proxies need to have the same version as the Zabbix server so you need to upgrade them as soon as possible.