For starters, TCP/IP works equally well in both operating systems. Other protocols of interest include:
Yes.
Tcp/ip
The network layer protocol is Trivial File Transfer Protocol (TFTP)
No you can use multiple protocols.
NDIS
protocols used for network device.
H.323 gateway. network + page 561
The Windows server OS has the ability to establish and manage a domain network. A Windows client on the other hand can only join such a network but not control it.
DECnet from Digital Equipment Corporation is a suite of protocols which may be used on large networks that integrate mainframe and minicomputer systems. It is a routable protocol. DNA - Digital Network Architecture.
These are called protocols - a standard set of rules for common communications across networks.
I'm not sure what you mean by "directly." Data can be transferred between the two through many protocols. Most networking protocols are platform-agnostic, meaning they can be sent and received on any network-capable operating system. If Linux has a Samba client installed, it can access files made available on a Windows share. If Windows has an NFS client installed, it can access Linux / Unix NFS shares.
Routed protocols are the best paths in a network along which to send network traffic.