Illustrator brushes are available from a number of retailers. Such retailers include any art store, such as AC Moore. They are also available for digital illustration software; digital illustrator brushes are available from Adobe.
Yes, just load the ABR file into Illustrator
If one wishes to download free Adobe Illustrator Brushes there are a number of options that are available. Free downloads for the brushes can be found on sites such as Tripwire Magazine, Vector Boom and Smashing Apps.
Yes, use the copy command and paste into Illustrator and vica versa. The shapes from Photoshop can be used as Illustrator brushes, Illustrator symbols, Illustrator paths and swatches. You can also copy Illustrator paths and use them as custom shapes etc in Photoshop - all are still vectors for any size of work
You can go to Deviantart to find brushes.
There is no such option in Photoshop. If you mean Vector Photoshop shapes then the shapes can be used for infinite things in Photoshop such as layers, masks, as frames, as a source for selections, as a source for actual brushes, for patterns, for exporting to other applications, used in shape blurs, used as cookie cutters in Photoshop elements. Illustrator vector brushes exist as do expression and Xara vector brushes and many others but sadly, as yet, Photoshop has no vector format brushes.
Nowhere. Once you sell your book, the publisher will find you an illustrator and pay them. Nobody works for free.
There are many places online to find Adobe Illustrator tutorials. Some of them are free and some of them are not. Searching for Free Adobe Illustrator Tutorials should yield some answers.
Badger brushes is the most ideal material for a shaving brush because of its water absorbing capability. Badger brushes come in a variety grades differing in price and quality. One can find more information about badger brushes online at Shaving 101.
Sally's Amazon
There are many listing sites for a freelance illustrator job. Linkedin is one of the opportunities. Anyhow it would be good to make a profile yourself there. Just like you are looking for a job, there are people looking for a good illustrator. Let them find you!
http://www.becominganillustrator.com
I am not sure if you can take a class for free, but you should be able to find a tutorial online for free. This will help you learn the basics of Illustrator.