How to provide different bleed to odd and even pages?

Do two sets of export, one with bleed right, one bleed left. For one set save as individual pages. Then open the other and replace pages. Bit of a pain if you have 500 pages...

Could you set up your files to include the bleed manually (creating an artboard for even pages, another for odd pages and duplicate them from there). You'll need to tell the printer to use the file "as is" and remove the bleed in the new document settings: (same can be found in the document settings after the document have been created)

That means that you will need to increase your sheet size by the bleed and either constrain your design within guides you placed yourself or even better create some margin by drawing a rectangle in the first two artboards and go CMD/CTRL+5 and make guides from that rectangle:

Effectively what you will be doing is creating two "master pages" (now called parent pages) like you would do in InDesign, and once they're done, just duplicate the two artboards to suit your page number.

Does it make sense?

You need it. The normal mix for anyone making a book is Photoshop (for photos and scans), Illustrator (for designs and illustration) and InDesign (to lay out pages, and add flowing text).  I wanted to emphasise that your work on art doesn't need to be redone, the illustrations are placed into InDesign, and can still be edited, then updated in the page. You should get some training in InDesign though, it looks like Word, but just diving in and using it as if it is Word will waste your time and energy enormously. In particular, you need to know how to use text styles - never change the font of text directly.

Use InDesign. That's what it's for. Indeed, though, nobody submits InDesign files. You make the work in InDesign and export it to PDF, submitting that - so the layout is finalised and locked, the fonts all included, all ready to print.