SMART failure on Hard Disk 0

Greetings everyone!

     So, about 4 day ago i got the dreaded black screen from my Dell 1537 telling me my hard drive was basically toast. Look like im going to be hard drive shopping. I will point out that my situation is a little unique, sadly i had a death in the family about 2 months ago and sort of inherited a laptop that was being used solely for a charity organization (which was routinely backed up until the individual was too sick to volunteer anymore). The reason i bring this sad story up is that im in a rare position where all i stand to lose on this hard drive is 3 seasons of The Wire and a few work files i was able to get transferred to my cell phone (literally all i had on this thing). Im trying to figure out what i should do from here, i know not to try to boot anything up so i dont do any further damage, but i will admit this will be my first time installing a hard drive (under the supervision of a few tech buddies who get a kick that this i a big deal for me). I have a few questions that are so stupid that i would not dare ask them for fear of being rediculed. So, please do not laugh, bare with me and if you want some major karma points please offer some genius advice for free.

Question 1: Can i use an external drive instead of installing an internal replacement drive? This seems appealing concidering these Dells get so stinkin hot that having to constantly use a bulky laptop fan is a headeache and im not completely conviced it definitively solves the problem (i swear the thing gets so stinkin hot even with the fan on full blast). I understand this could be a pretty dumb question but so far ive heard mixed advice from the wise and 100% reliable internet so if someone could let me know id appreciate it. So far the big issues ive come across was data transfer limitations but with firewire and eSATA data cable speed seems to be going the way of the Segway. My assumption is that an external drive most ilkely will not fix my problem since that would be too good to be true, but i am curious as to the specific differences between the two.

 Question 2: Recovery Disks.If i had a nickle for every time i had to use recovery disks to restore a laptop id be pretty stinkin rich, this i coming from a young man who, years ago, was proudly convinced anti-virus software was for suckers (im just realizing this is the first time ive admited that). However, As i stated earlier the last owner of THIS laptop was suffering from advanced cancer and is unavailable to question in locating the recovery disks. I was under the impression they were being stored with some other personal computer accessories, however they have still not turned up. Im really hoping that this isnt going to be a bigger problem than my hard drive. Is there a way to contact Dell with the laptop model number, etc? (i beleive i even have the sales receipt from when it was purchased since it was a tax deduction). My other fear is that trying to aquire these disks may be an excellent opportunity for the fine business executives at Dell to charge a rediculous amount of money for some cd-roms (which is kinda genius actually). So, if i cannot locate these disks, and yes im going to try real real hard, what do i do? There has to be a way to get them, right? Is it possible in this day of technology that a computer can be bested by a cd-rom? I sure hope not.  

Question 3: Lets be honest, this isnt exactly the cutting edge of laptops im getting ready to restore. If i buy a new internal hard drive for an outdated laptop im probably not gonna go nuts with space and RPMs. Everyone keeps telling me 500 gigs is just standard along with over 7500 RPms, and im usually the guy who buys expensive stuff when i really dont need it. Honestly, the stock hard drive that i had in this thing was just fine as far as space was concerned, and while it was nowhere near as nice a my mac in terms of speed, it got the info i needed in plenty of time. I guess what im asking is what does everyone think? How cheap should i be about replacing my hard drive? what kind of space should i be realistically shopping for? I have a mac mini, a Macbook, and a Western Digital external 1T for my important data back-up, so im really not hurting on space (im also typing this email on my DELL inspiron mini which feels like a very large cell phone.) I think we can all agree the price difference between an upgraded hard drive and the stock hard drive that came with the 1537 can be quite substantial.

Question 4: last one!! Okey dokey, so during the time i decide on the hard drive, locate the recovery disks, and brilliantly install everything swiftly, cleanly, and without a hitch; What do i do with it? Ive read im suppossed to keep it cold for some reason though not sure why. Ive gathered that constatly attempting to reboot and restart the computer probably wont magically cure the problem, but should i keep it charged? I seem to remember that letting the battery drain can be bad for laptops (or was that electric cars?), but once again, that's why im the "first time poster" and all of you are the geniuses that are here to help without being condesending. I'd greatly appreciate any advice anyone could give me with this issue, i gotta admit it was a pretty nice little lap top for a couple months and id sure be upset if it's somehow toast, it also has some sentimental value i guess, id hate to inherrit someones computer only to break it within a couple months.

        Thanks to all who read through my long-winded (but very entertaining) post!! Please feel free to answer every question promptly and send me a brand new hard drive as well as the recovery disks.......and a Segway too while we're at it. Hey, they could make a come back!