Firefox mobile next?
Firefox, on the other hand, would be a real browser, running Javascript rendering and Gecko on the phone itself, which would not be allowed.
That said, I don't understand why anyone would want Firefox anyway. The iPhone's limited memory and CPU would likely make Firefox nearly unusable, while extensions would eat away at what little free space was left. Firefox isn't optimized for the mobile space, and I can't think of any features it would provide that would make it a better choice than Safari (or, on Android, the built-in WebKit browser).
Why would someone want it instead of Safari? I'm sure lots of people use Firefox on their Macs too. Competition usually benefits us consumers.
Do I think we will see it on iPhone? Definitely not (I'm pretty sure both Apple and folks at Mozilla agree).
Is there any end-to-end security between my handset and — for example — paypal.com or my bank?
No. If you need full end-to-end encryption, you should use a full Web browser such as Opera Mobile.
Opera Mini uses a transcoder server to translate HTML/CSS/JavaScript into a more compact format. It will also shrink any images to fit the screen of your handset. This translation step makes Opera Mini fast, small, and also very cheap to use. To be able to do this translation, the Opera Mini server needs to have access to the unencrypted version of the Web page. Therefore no end-to-end encryption between the client and the remote Web server is possible.