As I remember many people post affiliate links on their marketplace(free to post) but if you planning to spam there, no its not allowed.
I would think each affiliate would have a different opinion on that. I would probably start emailing my affiliates to ask about it.
Should be no reason against it as long as you're not automatically forwarding users on. An eBay search application should be just fine.
Was just looking at that site when you posted it Im thinking on just paying a foreign developer through scriptlace.com - should be under $1000 to get a full application done.
The links to ebay have to be posted on your own website.... You can link from facebook to your own website, then use the affiliate link from there. From CJ TOS: So unless the thind party site gives you the permission, you are not allowed to do it.
My suggestion: create a new CJ account with an incentive/special program field filled out. Mention that you will be promoting advertisers through Facebook, that way eBay can approve or deny the promotional method. Don't add the note to your current account, or else it'll boot you out of all current programs while advertisers review your promotional method.
Would it be ok to redirect through my own website, or would TOS stipulate that they use would have to click again?
If you do a php or htaccess redirect, it'll still show facebook as the referrer. As I said, create an account with an Incentive/Special description filled out, mentioning that ads will be place inside of facebook. When advertisers approve your application, you're good to go & in compliance with CJ's TOS.