NB: regarding addresses, I assume you're asking about unicast addresses.
"Can you know a machine’s location from its IP address in general? MAC address?"
In general, no, but sometimes yes.
Public IPs are assigned to entities, and you can sometimes identify some geographic region where an entity's network is, but how they assign specific IPs is up to them.
By default, MACs are globally unique, but sometimes the burnt-in MAC is overridden with a locally assigned one. When that's done, sometimes the MAC in encoded to indicate some geo location, but again, that's usually only known to the entity that did the (local override) assignment. Plus, MACs are lost at the first L3 hop.
"Can you identify a machine by its IP address? MAC address?"
Unsure what you mean by "identify". By default, global MACs are assigned to NIC vendors, but that doesn't indicate the host it may be installed in, or whether it's really the original burnt-in MAC.
"Can two identical IP addresses co-exit? MAC address?"
Sure, also more than two, but usually not so assigned where the same IP or MAC is "visible" to the domain it's being used within. If such is the case, then the network wouldn't know where to direct traffic to a specific IP or MAC.
"Can you use the same IP address when you travel to another city? MAC address?"
IPs, usually not, but there are exceptions. MACs, often by default, yes.
