"There is two partitions we will be backing up and restoring.
One partition is 320GB
Other partition is 810GB
I'm going to create a policy to backup both partitions and
turn multiplexing office. This will create two streams on
the backup. What about the restore? How many streams?"

It will only create 2 streams if you use the directive, but that's the right 
idea.
 
"Also, Could I get better performance by creating a policy
that would do the following:
 
partitionOne/dir1
partitionOne/dir2
partitionOne/dir3
partitionTwo/dir1
partitionTwo/dir2
 
I realize that I will be spindle bound by the disks on the
partition, but how much will this speed up the overall
process of backing up and restoring?"

Depends on the type of disks, number of them per LUN, and connection type to 
system.  Most likely you would be best served by just doing it at the file 
system level.  At 20MB/sec it would take about 7 hours for the larger one to 
complete.  If there's a clear logical separation in that larger file system 
maybe split it into 2 streams, but no more.  You're just begging for disk 
contention at that point.
Having said that, if you have 20 15k fiber channel drives that you've carved 
these file systems from, by all means create the 5 streams.

~JK