Fairing recovery was asked in the press conference afterward - here's a transcription from r/spacex
Fairing recovery has proven surprisingly difficult. I'm still fairly sure we can do it in the next six months, but the fairing is [not aerodynamic], messes with the parachute... we also have a fairing version 2, much more important than version 1 fairings.... my guess is next six months for fairing recovery. We have the special boat. .....we might even be able to catch the dragon too, if nasa wants to
They're actually huge expensive carbon fiber things. Think "racing yacht hulls", and cost several millions of dollars each. A significant portion of the cost of the whole vehicle.
Plus they're slow to manufacture, so they can increase tempo if they can get them back intact.
I think they cost on the order of magnitude of $1M each.
As I've heard it been put - "Imagine if there was a pallet of $1M in cash falling from the sky. And you knew where and when it would fall. And you'd expect the rate of 'cashfall' to increase to tens, even hundreds of times a year. Would you try to develop a system to catch it?"
The profit equation is a little bit more complex. Consider that recovered fairings would be used multiple times, not just once each; and the long time to manufacture each new one adds an unwanted scheduling delay.
Imagine building a shell big enough to hold a school bus, capable of withstanding hypersonic flight through the upper atmosphere, and protecting an extremely delicate payload from outside noise so loud it causes the waveform to clip because the troughs become vacuum.
The fairings are troublesome for several reasons. They have to be very large because they have to be larger than the payload, they have to be very strong because they have to protect the payload through the atmosphere at supersonic speeds, and they have to be very light because they ride on the upper stage, and their weight takes away from payload weight (not quite at a 1:1 ratio but not too far from it). So they are expensive because expensive fairings allow you to launch even more expensive payloads.
And in principle they are not terribly difficult to recover. The re-entry speeds are fairly low since they are only ever sub-orbital, and they are very light for their size so re-entry heating isn't a major challenge. But aerodynamically controlling them in a reliably manner to a precise location seems to be a problem.
In addition to the several million dollar cost of the fairings they represent a production bottleneck - they're carbon composites which take a long time to make and require very expensive tooling. No matter how many reflyable first (and maybe in future, second) stages spacex has in stock, if they can't produce fairings fast enough they cannot go to space.
Aside from the actual costs involved in (lengthy) labour and materials, manufacturing fairings also takes up vast amounts of factory real estate.
The numbers are small compared to the rest of the game, but it's one of those things that would make life so much easier if they could just catch the damned thing.
Even being a seemingly simple structure it would still be expensive to build. I'm sure it also contains latching hardware, etc. used to release it. Seeing as it's mostly a static piece if they can get it down in one piece it's probably "trivial" (compared to a full core) to re use it, but it saves money (and junk in the ocean)
The fairing doesn't get carried to orbit. It's dumped as soon as aerodynamic loads are negligible.
Since the fairing has the same energy requirement as the payload (in energy/kg), it's important to get rid of it the moment it's unnecessary. If they took it to orbit (so they could leave in space), it would drastically cut down payload mass.
First off, they aren't lifted to a stable orbit, that'd cost additional fuel (which'd need more fuel again). They're detached once the air is thin enough that the resistance doesn't cause problems. Secondly, it'd also clutter space further.
They had the ship done and seemingly ready back in December - https://imgur.com/gallery/MQcEE