The only way you can linked is if you log into your banned account and new accounts. Also, don't use the EBay/PayPal apps.
As above, definitely don't use the eBay app. Also, I would always upload those photos and strip the EXIF data before uploading photos to eBay from your computer. You can never be too careful with eBay.
I have a new iPhone. It has my Facebook App etc on it. Will Ebay link me to old accounts via my new phone?
I'm not sure how the Facebook app fits into your question but no not via Facebook.
Are you using the eBay/PayPal app? Is so you could be linked this way. It's better to use a mobile browser if you want to use your iPhone to manage your accounts.