1) How do switches without "ip default-gateway" configured respond when a ping is initiated from the switch to an ip address that is not in the same local subnet as the switch's management vlan? Does it do a proxy arp for the ip address?
2) If a default route has been defined in the routing table, will routers with proxy arp enabled answer to arp request for ip addresses that do not belong to any network found in the routing table?
Eg. RouterA's routing table contains connected interface and routes to some local subnet. In addition, it has the default route (to Internet) configured. If it receives an arp request for an Internet ip address, will it answer with its ethernet mac address (proxy arp)?
Yes if the switch ARPs out the interface for any remote destination the router on the same subnet would reply with proxy ARP if a specific route to the destination or a default route exists in it's routing table.