Paint.NET is a Simple,free and a powerful tool, if you need something more feature packed, check out GIMP, though, i would recommend trying Paint.NET first, you'll probably be satisfied, You can get it on FileHippo and many places, just google it.
There is no alternative. The closest you'll get is GIMP, which imho has a crappy unintuitive UI. But it WILL do pretty much all the basic stuff that Photoshop does.
I think the best alternative to Photoshop would be GIMP. However, Photoshop is still the easiest to use in my opinion.
gimp also has a bigger brother called Gimpshop, which is essentially the same, but someone has changed the UI to more closely resemble photoshop. Not sure if it is released for Windows though as I have it for Linux.
I used GIMP for the first time last week. for college i had to do some sort of software comparison and do basic things like change image colours, make a collage, move things around etc. anyway i compared it with GIMP, downloaded it etc and to be honest i was really impressed with GIMP and with the intuivity (if that is even a word!) and it was pretty good. if i was not going to bother getting a dodgy copy of photoshop, i would definately use GIMP. Good program and free!!
Why do you need alternative? Learn Photoshop, its quite easy to grasp and its industry level and can do wonders.
Illustrator has become the biggest replacement for Photoshop. Now, most of my friends are using illustrator rather than Photoshop.
Yes it is to some extent but Photoshop is still the king. But all softwares have their own specialty. Illustrator is best known for vectors illustration and especially logos. I design all my logos in Adobe Illustrator.