In general? Or in this particular case?
I'll answer both...
IN GENERAL
If you have 1 router with 1 subnet and 3, 5, 10, 15 workgroups all with the same IP address scheme
(192.168.1.x) then, yes, you:
1) Will be able to see hosts sharing no matter what the workgroup (XP, 2000, Vista, 7, 03/08 all included)
2) Yes
3) Yes, or like in XP and below, you can actually browse to them via My Network Places > Entire Network > Microsoft Windows Network > Then it should show all domains and workgroups in the LAN or WAN that contain hosts that have file/print sharing enabled... now, whether or not you will be able to access those hosts is up to how they are shared (Your username and password may/may not have read/write access to those hosts.... setup from the host)
3... extended) A short way to avoid finding out through a network map which host is in which workgroup or domain, yes you can use a UNC (\\host\share) and you should be able to connect (given that you LAN or WAN is physically setup in a fashion that enables you to physically)
The long and short of workgroups is... they dont matter, they were originally created for organizational purposes only and they do not hold, nor can they hold, permissions sets. Simple reason being, workgroups are used in a peer to peer environment or a domain/peer to peer mixed environment. Those in the peer to peer environment that are in a specific workgroup hold all of their permissions on their own local node or workstation (folder/drive sharing permissions) Workgroups just makes nodes easier to locate in a multi-workgroup (but still all peer to peer) network. The "Workgroup" or "Domain" will hold permission sets and then appear to deny certain people/groups/computers/other domains from them only when the domain controller holds the permission sets for domain... thus, all permissions are held in active directory (or similar perhaps in a *nux envirnment) And in this case, it's a domain and no longer a Peer to Peer network
and in this final case, the workgroup is no longer defined in a workgroup...it's a domain at this point.
In a peer to peer network, nodes
never have to be in the same workgroup in order to share files/printers with each other.
THIS PARTICULAR THREAD
E.g lets say I am a user in workgroup A. Will I...
1. Be able to 'see' hosts in workgroup B on the network
No, because the only node in WorkgroupB has file and print sharing turned off
Also, no because it will be behind the second router's NAT***
2. Be able to ping any hosts in workgroup B from workgroup A (and I think I should be able to)
No
Only because the node in workgroupB is behind the second router's NAT***
3. Connect to hosts in workgroup B from wg A (as in \\computername in address bar)
No, again, because file and print sharing is off on the the node in workgroup B
***Now, if there was a 0.0.0.0 static route setup
An ICMP request will be able to be returned from the node (unless rejected by a firewall) because the ping has nothing to do with file and print sharing, but you still would not be able to see the node due to file and print sharing being off on the node
If the static route existed and the node in workgroupb had file and print sharing turned on but just in a different workgroup? Sure, absolutely.
Hopefully that covered your question, sorry if I confused ya...
If you have any other question let me know because sometimes I can explain it in more detail with a more direct question