1: The blue light on the drive should be on when the drive is reading or writing, otherwise it will be off. Miscellaneous Windows functions (such as AutoPlay) may occasionally cause it to flash, Windows indexing the drive for faster searching will make it flash, etc. but for the most part if you aren't doing something involving that drive it will be (mostly) off. That is all normal.
2: The delete key works great, but the total size of the files is usually going to be too big for the Recycle Bin, so they will actually be deleted with no means to recover them from the Bin (after-market programs might be of help for that). So be sure you really have everything you want backed up.
Sorry to hear you had trouble with the drive. I have been lucky so far in that all of mine have worked out of the box. I wish that were true of every computer component I have purchased, but that is not the case so I understand any frustrations you might have. PGM will fix it for you, you can count on that.
Good luck.
By the way, if you haven't tried another usb cable you should. Seems to have worked for some folks on the forums here in fixing similar problems to yours.