There is no download for 10.4.x or 10.5.x, there is a very slim chance you can get 10.5 by calling Apple, but usually you can only get it on eBay & such.
Tiger Requirements...
To use Mac OS X 10.4 Tiger, your Macintosh needs:
* A PowerPC G3, G4, or G5 processor
* Built-in FireWire
* At least 256 MB of RAM (I recommend 1GB minimum)
* DVD drive (DVD-ROM), Combo (CD-RW/DVD-ROM) or SuperDrive (DVD-R) for installation
* At least 3 GB of free disk space; 4 GB if you install the XCode 2 Developer Tools (I recommend 20GB minimum)
http://support.apple.com/kb/HT1514
http://www.ebay.com/sch/i.html?_nkw=mac+os+x+tiger+retail+10.4
See Tom's, (Texas Mac Man), great info on where/how to find/get Tiger...
https://discussions.apple.com/thread/3089008?answerId=15305521022#15305521022
Or Ali Brown's great info on where/how to find/get Tiger...
http://discussions.apple.com/thread.jspa?messageID=10381710#10381710
Leopard requirements/10.5.x...
* Mac computer with an Intel, PowerPC G5, or PowerPC G4 (867MHz or faster) processor
minimum system requirements
* 512MB of memory (I say 1.5GB for PPC at least, 2-3GB minimum for IntelMacs)
* DVD drive for installation
* 9GB of available disk space (I say 30GB at least)
Classic/OS9 Apps no longer supported.
May be available from Apple again...
https://discussions.apple.com/thread/4720126?tstart=0
Trouble is Apple no longer sells it, check eBay & such for the Retail version, not the Gray Discs...
http://www.ebay.com/sch/i.html?_nkw=mac+os+x+leopard+retail+10.5
Now, for your Trash problem, see if this helps...
Solving Trash Problems...
http://thexlab.com/faqs/trash.html