I'm trying to understand the TCP transport layer protocol,
specifically related to how packets are sent.  Please answer, in
detail (to someone who is trying to learn TCP), the following
questions:

What is the maximum possible window size for TCP?

Assuming that the round trip time of a network is at least 2 seconds. 
What transmission rate is needed in order to transmit a full maximum
size window before it would be possible to receive an acknowledgement
to the first bytes in the window?

Assuming a transmission time per packet is 20 msecs, the size of the
window size is size x at time i, the propagation delay from source to
destination is p, there are infinitely many packets to be sent, and
the window size is exponentially distributed, what is the probability
that there will be a break in packet flow when all the packets in a
window are transmitted?