WN2500RP (Devices Served By)

What a strange way to have Internet access.  I'm sorry to say but this is a horribly insecure, and probably slow, setup.  

The problem is that your WN2500RP isn't providing you with any addtional security.  The WN2500RP doesn't have a firewall, so your devices can still be reached by anyone on the network.  Plus, when your traffic crosses over from your WPA2-protected Wi-Fi network to the WEP-encrypted network, anyone with the WEP encryption key can capture it with the right tools.  If your traffic is not encrypted at the IP level, then they can see what you're doing.

You really should get your own dedicated Internet service.  If that's not possible, then you have to do much more to secure your own network.  Either way, you need something with a firewall to keep your neighbors out.  All consumer-grade Wi-Fi routers have firewalls, so you could get one and plug it into your WN2500RP.  Or get rid of your WN2500RP and replace it with a router than offers a WAN connection through Wi-Fi, but these routers are not as common (Exception: Routers running 3rd-party firmware like DD-WRT and Tomato can do this).  Note: Once you put your own router in place, your traffic will be double NAT'd.  This isn't ideal and could cause problems, especially with online games, but that's the price you'll have to pay to continue using the condo's Internet service.

The firewall will keep your neighbors from getting into your network, but it can't do anything about protecting your traffic from being snooped while it transits the WEP network.  To counteract that, you will need to encrypt all of your traffic.  A VPN service will do just that.  Do a Google search for vpn providers and pick one that suits your needs.

I hope this helps.  Now to answer your questions.

A1: Extenders don't filter by IP addresses.  Only devices that have your WPA2 key can connect to your extender.  But it doesn't matter whether anyone can connect to your extender or not.  An extender doesn't have a firewall, so anyone connected to your condo's router can reach your devices.

A2: Irrelevant question.  See A1.

A3: Irrelevant question.  See A1.

A4: Yes, the Sony probably won't show up directly in your Wireless Network Watcher when it's hard wired.  Traffic from the Sony will "appear" to be coming from the extender.  This is why you saw multiple IP addresses with duplicate MAC addresses.  Someone else with an extender or router will also exhibit the same thing.

A5: No, the DCH6200 does not appear to have any Wi-Fi capabilities.

A6: Liteon makes Wi-Fi adapters.  Disregard the hype about power cables having Wi-Fi chips in them.  That's bogus.