Irfanview actually has a feature to make a DVD (or CD) slideshow automatically when you put it in a PC, but I haven't played with that.
Re: dual layer. I think you'd have a very hard time finding a burner that
won't do dual layer at this point. But I wouldn't recommend dual layer blanks just because they're at least 5x the cost for less than 2x the storage. (about 8.5 vs 4.7.)
Re: DVD vs hard drive - no question, DVD. Hard drives are far less reliable. Plus there's the whole "eggs in one basket thing" - if your hard drive fails completely, you lose all your backups. And chances are that because you're only using it for backups, you won't notice if it's getting bad sectors before it fails completely.
Re: storage. A single-layer DVD actually holds more like 4.35 gigs than 4.7. One of those "different ways of counting" things you hear about.
Re: viewing from CD/DVD. It's really not convenient to view from disc, first off it's slow (especially if you look at one picture long enough for the disc to spin down, then you have to wait for it to spin up again) and there's little organization. I would treat CDs/DVDs as backups and view from the PC. The exception would be making a disc to view on a DVD player that can view JPGs, in which case you'll want to organize your photos in folders.
Re: age... if your PC and hard drive are seven years old, you are
definitely on borrowed time! You need to back your stuff up immediately! Yesterday even!
If you are even somewhat competent with a screwdriver, you can replace your existing CD/DVD drive with a DVD burner yourself. A quality DVD burner costs all of $30 or so from NewEgg. If you want an external, it will be slightly more - and again, make sure you have USB2. A USB2 add-in card is cheap, like probably $10-15.