1. ¿Who is assigning it that IP? ¿Why .135?
Your question suggests to me to that you were expecting the IP address to come from the DC (192.168.1.10), which is a bit unclear in the layout unless the DC is the box that connects to ESX 1 through vmnic0 (which means the DC is a VM running inside ESXi 1). It looks as though the XP got its IP address from the VMnet2 switch as it also has DHCP functionality. So if the DHCP scope of the VMnet2 includes 135 and the DC DHCP scope is different, that means it got its IP address from VMnet2 virtual switch. Effectively there are two DHCP servers in the same network. That is just the nature of it, AFAIK, whichever DHCP server responds first to a DHCP address lease broadcast will assign the lease. Just make sure that the DHCP scope of VMnet2 and the DC doesn't overlap.
2. ¿Why can I ping successfully to ESX1 and ESX2 but not to vCenter? In fact, XP should be isolated from ESX2 and vCenter.
It is likely firewall rules of the OS that vCenter runs on that is preventing the ping. If it is Windows usually incoming ping is blocked. If you want to allow ping you can add this in the firewall rules. Run this using Command Prompt Admin (or you could manually through the Firewall settings GUI)
netsh advfirewall firewall add rule name="Allow Incoming ICMP" dir=in protocol=ICMPv4 remoteip=192.168.1.0/24
To delete the rule above
netsh advfirewall firewall delete rule name="Allow Incoming ICMP"
3. In vSphere console, "Management Network" is the only that has "IP Settings" tab (apart from "General", "Security", "Traffic Shaping",...). ¿Why is this so?
Only the Management Network would have an IP address as the other networks (VMNetwork) are just virtual switches. As the name sort of implies, it is to manage network settings of the ESXi server itself. The other networks are just virtual switches. I suppose in a real world implementation, the ESXi will have a fixed IP address and the VMs running inside (a physical) ESXi server, depending on its role, will either have a static IP address (for example, a DC) or have it assigned dynamically through DHCP (such as through a DC which could be a VM or running as physical machine just like the ESXi). The ESXi server itself can even join the domain. Maybe you can try later on to make ESXi 2 as part of the domain running inside ESXi 1 (now this is becoming convoluted very quickly).