Can I transfer eBooks from my iPad to my Sony eReader? If so, how?

It depends on what "ebooks" you mean. Electronic books from most sellers - the iTunes Store, Amazon, and Barnes and Nobel, for instance - use a proprietary format that works only in that vendor's devices and/or software. Other sources that provide books in an open format would probably work. Sony's web site should tell you what formats the eReader can accept.

There will also be the issue of how to transfer books from the iPad if you don't have a computer. I don't know of any way to do that with a Sony reader, but there could be a workaround using some web-based service.

Regards.

That will not work. You can download an eBook into a supported ereader app (Nook, Kindle, Kobo, Sony if they make one) on the iPad, but the only way to get it onto another device would be to transfer it off the iPad onto a computer. Then use Adobe Digital Editions or OverDrive (depends on how the library distributes their loans) to move from the computer onto the other device.

There is no way to transfer a file directly from an iPad to a Sony ereader (or any other mobile device for that matter). You would have to use a computer as an intermediate storage place for the ebook.

Just my opinion, but as nice and useful as the iPad is, it in no way is a true replacement for any of my computers.