Hey guys...let me offer up a bit of my input since I happen to run a fairly large mobile affiliate program and mobile solutions provider.
The answer to your initial question about how mobile converts is pretty much already in this thread...just spread across a few different posts
Mobile billing can absolutely convert better...but there are a a lot of variables to consider.
One of the most important variables is carrier billing versus credit card billing.
The obvious reasons that carrier billing converts significantly better than credit card in most cases is because of the smaller price points and the simple billing process (typically one or two click billing).
So when carrier billing is available, most users choose to go that route simply because it caters to the impulse buy...the quicker and easier it is to pay, the better.
I would argue that mobile redirection is still very valuable and with all the new tools and tech that companies like mine and my competitors have come up with...there are still really solid ways to redirect mobile traffic despite all the Google Mobilegeddon crap. It's still the bread and butter for my mobile affiliate program...outside of the mobile billing solutions that we offer.
Now there are definitely exceptions to this...cams sites would be a good example.
Typically many cam sites have larger price points and a billing structure that most mobile carriers wont approve. However, we provide carrier billing for 3 large cams companies and they do fairly well by playing the numbers game...very low margins, but very high volume of users paying by mobile.
Some other major variables to consider (out of many variables) is the actual site design, the country, and the traffic sources.
Some countries have very strict rules and regulations about what level of content you are allowed to show...or they have rules about how the user should be billed and how transparent you must be with all of that.
This can dramatically affect the user experience and cause many mobile sites to have undesirable results.
Responsive design is not always the way to go (in most cases in my opinion)...I've seen the most success with companies who build a site specifically for each device. It is much more work and can be harder to manage, but it is totally worth it in the end.
Keeping in mind that credit card billing can still work quite well on mobile sites...mainly because you are not regulated by the mobile carriers when you don't use carrier billing.
In these cases where you want to see your mobile site perform better while only using a credit card billing solution, then there needs to be a heavy focus on the product and the quality of traffic.
The truth is, this is a topic that is way too robust to go into in writing, especially here on a message board...it's definitely something that should be discussed more in-depth.
As I mentioned, there are SO many variables that no matter what valid points I make, there will always be exceptions and there will always be other valid points to argue the case

There is also the fact that almost every 3 months there are dramatic changes occurring in the mobile space that require us to adapt or evolve at a rapid pace...which can be quite difficult if it's not something you do full time.
Anyways...sorry for the longwinded message. I just wanted to confirm what a few people here had already said as well as add my two cents.
If anyone cares to learn a little more about the basics of mobile, then take a look at the education article I wrote for the GFY Educational Series:
https://gfy.com/gfy-educational-serie...-8-mobile.html
Catch you later dudes!