This looks like a budget home type printer. My Canon laser printer (see picture) has an open paper feed tray like the picture. It can be folded up when empty, and for packing and transport, and looks like a "door" but you have to have it folded out and lying flat to hold the paper. Otherwise you cannot print. A lot of budget laser printers are like that. Likewise the paper output is a flap too. Close that and the printer will jam! You don't get fancy trays at these prices.
As for the driver CD you can get a download from the HP website which says "HP LaserJet P1005/P1006/P1500 Printer Series Full Feature Software and Driver: This full software solution is the same solution as the in-box CD that came with your printer." It says it works on Windows 7.
By the way this Canon was a bargain! Brand new 48 UK pounds, plus shipping 5 pounds, about 75 US dollars, and it came with a full capacity 2,000 page toner cartridge (not a smaller starter one like some brands) which has not yet run out. We don't use it a lot. I got it in July 2008! I can get a compatible re-manufactured cartridge for 12.99 pounds, about 20 dollars, or a bottle of toner to do my own refills for about 5.70 pounds, 9 dollars, but I don't fancy doing that really, having seen a few toner disasters at work. For mine you have to make a hole in the cartridge and insert a plug after refilling. You can buy a thing like a soldering iron to melt the hole. A re-manufactured cartridge is cheap enough.