2. This is a common newb question, the answer is no. microsoft isnt that stupid, the purpose of installing the games to your hard drive (about 6 gigs a game) is to make the game run smoother and load faster while your playing it. makes it so the disc doesnt have to spin as much and its less wear on your disc drive over time. get a 60g or 120g hard drive if you plan on doing this cause a 20g hard drive will fill up faster than you think.
3.Buy a refurbed hard drive and you wont have to worry about it cause it should be wiped clean. or if you buy from a private seller ask them if they had the contents transferred onto their new hard drive. i have an empty 20g at home because i bought a 120g and it came with a cord that transfers your old to your new and wipes the old clean. there really shouldnt be any software on it you need that u can delete though, when u put it in your system if it asks you to do a system set up then ur fine, if not, goto the memory option and delete any personal setting or profiles on the hard drive and restart your xbox and hopefully it asks u to do an initial setup.
4.20g refurbed from a gamestop can go for 59.99 but check out ebay, i see them there for 30. 60g goes for around 55 used.