is it necessary to have 2 computers to use Armory's wallets?
No.
I am new to bitcoin and still trying to understand how to a) purchase bitcoin, and b) store it safely.
There is an exchange nearby whereby i can physically purchase a paper wallet which they print for you on an offline computer and hand you the hard copy code and a usb stick copy. They charge 5% for this service.
If i buy coins his way, is it difficult to 'transfer' them into an Armory or other wallet in an offline computer?
No. It is easy. I wouldn't however see any advantage worth paying an extra 5% to transfer coins using this method.
Final question - if i buy for example 5 bitcoins from this exchange and am given a paper wallet with the 2 keys, how can i then transfer (safely) a samll amount of that bitcoin, say $500 worth, into a hot wallet that i can use to make transactions with?
Apologies for the basic questions but i'm still learning!
Any public address holding funds can make transactions if you have the private key. However, I wouldn't recommend transferring coins to, or using a public address where you were not the individual to generate the keys (i.e. the paper wallet given to you by the exchange). What you'd want to do is load the coins into your software wallet by importing the private key from your paper wallet, and then send them to an address you have generated yourself. After that, you could delete the imported private key.