[Of course, the feature here has been based on the latest build 10149 of the OS - it's possible that some things will change before the final release. Just sayin'....!]
What camera applications come with Windows 10 Mobile?
It depends on which device you have - it seems that the 'Nokia'-branded phones above a certain specification will retain 'Lumia Camera' (in fact, in the current build it's still called 'Nokia Camera' initially, until it's replaced in the Store with the new name), as well as 'Camera', a clear derivative of Lumia Camera 5.x but adapted for as wide a device pool as possible. Lumia Camera contains extra 'smarts' that know how to handle the extra microphones and optics in some models.
However, Lumia Camera for Windows 10 Mobile ends up as v188.8.131.52, i.e. exactly the same as you're currently using under Windows Phone 8.1. So it seems as though you can carry on as before - nothing need change.
Interestingly, (Windows) Camera gives its version number as v5.38.2004.0, indicating an evolution of Lumia Camera 5 (still on v184.108.40.206 on the Lumia 930 etc.), though it's clever enough to handle each device on its own merits in terms of 'Rich Capture' - the 1020's mechanical shutter and slow capture mean that this feature simply wouldn't work - and so it's not offered.
So I can carry on using 'Dual Capture', PureView zooming, 'Reframing', and shooting RAW?
Absolutely. Your default camera is set to Lumia Camera (v4) still, and all the same options are there in the interface, settings, and even the hooks from Windows 10 Photos into Lumia Creative Studio (which hasn't changed). Ditto shooting RAW (.DNG) files and sucking them out via cable with Windows Explorer, Nokia Photo Transfer or similar.
It's business as usual!
What happens if I use (Windows) Camera instead? Is snapping much faster?
This (Camera) does start fractionally quicker, though it's still three seconds before the viewfinder is fully live, so there's no significant gain. And, probably due to debug code still in place, there's a noticeable shutter lag at present on the Lumia 1020. PLUS, it always capture at the maximum resolution of the sensor - and I suspect that you don't really want to be snapping 10MB 34MP images all day long, so you can discount this application for the 1020.
The big misconception was that a next generation camera application would somehow speed up the 1020 camera dramatically, but (short of a low resolution scrape of the sensor) the bottleneck is still grabbing 38MP worth of data and then saving it. So you'll have to live with the 1020's (lack of) speed and, as usual, console yourself with quality!
Will Lumia Camera stay available throughout the 1020's life and Windows 10 Mobile?
Admittedly this app has disappeared a few times in the past year in the Store for some devices, but these have only been temporary lapses - there's no reason to suspect that it needs to be withdrawn for any reason in the long term. And even if it did (get withdrawn), 'Nokia Camera' is still part of the firmware builds provisioned for the 1020, so you'd always have this to fall back on, with much the same functionality.
And even if the above wasn't enough for you, other third party camera applications continue to work well under Windows 10 Mobile - I've been testing 1Shot and ProShot, but I'm sure the multitude of (less serious) camera apps will work fine too.
What about video capture? And what's all this about 'Digital Stabilisation'?
There's an odd setting in the simplified pane in (Windows) Camera for Windows 10 Mobile - a toggle for 'digital stabilisation'. Which seems somewhat unnecessary given the massive, famous ball-bearing OIS integrated into the 1020 camera. My guess is that this is intended to help on the budget smartphones which lack OIS and that it should be hidden when the application is run on more capable devices.
However, never one to rely on a guess when I could be testing it for real, I pointed my test 1020 out the window and 'zoomed' in on detail in a house about 200m away, looking at the stability under both applications:
From what I see above, the 'digital stabilisation' setting does nothing whatsoever on the 1020 - which is what I'd want, since OIS is going to be superior and you wouldn't want two stabilisation systems 'fighting each other'... Phew!
So the bottom line for imaging is that nothing will really change. Of course, Windows 10 Mobile as an interface and OS has improvements galore, but mainly for the higher resolution screened phones and the newer chipsets. On the Lumia 1020, the OS is a bit of a 'curate's egg' at the moment - but I suspect that optimisations for the 720p and 768p screens (and lower) are next on Microsoft's agenda, so I'll keep this 1020 up to date and report back.
There are no major showstoppers to anyone else upgrading to the Windows 10 Mobile Insider build on the 1020, but equally there's little reason to do so in the first place. If I were you I'd wait for the official over-the-air 'preserving all your apps and settings' update in September or October.