MS Paint + Irfanview (free). Create the icon in MS Paint at whatever size, save as BMP them open with Irfanview and save as *.ico, you can even choose the transparency colour in Irfanview.

 

Theres a free Photoshop plugin that can save files in .ico

EDIT: found it click

 

I am not sure. But its worth a try.

 

It doesn't mater, it depends on what size you made the image at, if it's 16x16 pixel image it will save as 16x16 resolution. You can get programs that scale your image to 16x16 or 32x32 but it's no different than shrinking it manually before saving. Basically it's no different to JPG or BMP, your icon will be whatever resolution you save it at.

 

I remember someone posted this up a while ago:

http://tools.dynamicdrive.com/favicon/

 

Thats what I do to.