So I assume my ISP has a DHCP server that gives us some dynamic IP and we are connected via PPPOE (username/password) but how is the subnet mask 255.255.255.255.
The subnet mask would tell the source host whether a given destination host is local (has its own link-layer address) or remote (must use gateway's link-layer address).
But PPP is a point-to-point connection – there is no ARP, there is no link-layer addressing, in fact there is no distinction between local and not-local hosts at all; there's only one place a packet could go (the other end of the PPP link). Because of that, there's no need for a subnet mask.
(A subnet mask can still be specified when configuring an address on a point-to-point interface, since it just acts as shorthand for a route via that interface – but it's not needed for the link to work at all.)
For the same reason, PPP links don't need a valid "default gateway" IP address either – the route can simply point to the interface itself, it doesn't need to be translatable to a layer-2 address.
Q# 1 - Now can PC connected to my router which has a subnet mask of 255.255.255.255 connect to PC3 connected to router1 which is another home taking internet from the same ISP with random IP and subnet mask of 255.255.255.255 connect?
The subnet mask doesn't matter. Either way you send the packets to the ISP's gateway, which forwards them to your neighbour's router, that's it.
As for whether double-NATing ISPs actually allow such connections between customers, I have no idea at all. Maybe if you try to connect to router1's WAN address, it would just work like normal (port-forwarding and all)?
Q# 2 - Can I also set the same thing in my router DHCP to give subnet mask of 255.255.255.255 to all the devices connected so they can not communicate in LAN but directly to the router?
In theory, yes, but not all operating systems will accept it. (IIRC, at least Windows insists that an Ethernet-like network needs to have an Ethernet-like subnet mask.)
Networks which want to enforce that all communication must go through the router usually take a different approach – they use "proxy ARP" on the router, together with "port isolation" on Ethernet ports. This tricks all hosts into thinking that every IP address in the subnet corresponds to the router's MAC address, and you get the same result.
Q# 3 - Will giving that subnet mask affect the performance of the network?
Yes – your router becomes the bottleneck for all internal LAN traffic, which can no longer take the shortcut through Ethernet switches. (Especially if routing is done using just the router's weak CPU.)
Although it doesn't directly affect your Internet access, the extra load on the router will still have a negative effect indirectly.
Q# 4 - Is the static IP that shows in "What is my IP" also possibly the Static IP of other connections that ISP has given?
Yes – if it weren't shared, there wouldn't be any need for the ISP to assign 10.x addresses to your router (they would have assigned the public IP address directly to your PPPoE link).
However, that has nothing to do with the netmask at all.
Q# 5 - Am I double NATTED?
Yes. Your router does NAT, and it has a 'private' WAN address, which means the ISP must be doing NAT, otherwise you couldn't reach the Internet.
if yes how much does it put the latency in a local connection?
I don't know.