There isn't a simple yes/no answer to your questions, but I'll give it a shot. But be aware that I have no knowledge of what Adobe are up to and that some of the things for Amethyst/Ruby haven't yet been implemented
So, on Amethyst vs FlashBuilder (FB): FB was designed to support Adobe's Flex platform and with that going away from Adobe, they now have no incentive to develop it further. They've said that they will release another version (with I guess what they've got in the pipeline included) but as for any further development ... ?? I just can't see that Adobe can make any money from FB, so you might want to draw your own conclusions about that. Also, it's worth pointing out that Adobe have decided to drop any GUI designer support from the next version of FB. See here: http://www.itwriting.com/blog/5240-adobe-discontinues-flash-catalyst-clarifies-flex-and-flash-builder-futures.html
On deployment: Amethyst does support build deployment into Android and iOS, but we haven't updated the scripts for the latest AIR and Android SDKs. If there's a requirement for this (and to be honest, we haven't been overwhelmed by requests for deployment features) we'll upgrade. The mechanism is there (it's part of the MSBuild system that we've implemented) and it won't take much to bring it up to date.
On calling ActionScript from Ruby: we're working on that. As you know, we've got both Ruby and ActionScript development environments and it's one of our primary goals to bring the two much closer together. One of the things that Ruby is sorely lacking is a front end (there's some GUI stuff in the Ruby libraries, but it's nowhere near usable, IMO). I don't want to say more until we've got something working and demonstrable, but being able to drive a Flash front end from Ruby is a high priority.
Amethyst vs. FB: well, (as a totally unbiased observer), I'd say that Amethyst has a future. We are absolutely committed to it and it forms the fundamental basis of what we do. In fact, we're currently re-engineering all our Ruby code to use the Amethyst code base. In contrast, I'd have to say that I don't think FB is in any way fundamental to Adobe ... they might continue to develop it or they might not. Either way, it will make no difference to them ... on the corporate radar screen it's hardly a blip: for Adobe, it's Flash CS5 that's the real money maker. Functionally speaking, Amethyst has a better debugger (and our new debugger 'bubble' system is miles ahead. However, FB has been around longer and has better integration with other Adobe products. Otherwise, they are pretty similar ... except that Amethyst is Visual Studio based and FB is Eclipse based. If you like Eclipse go for FB, if you like VS, go for Amethyst.
On the visual designer ... in contrast to Adobe, we think that visual design is important. We're currently reworking our designer to incorporate all the lessons we've learnt from our first go (which even in its current state is a lot better than Adobe's) and this new designer will form the basis of both Amethyst and Ruby visual design.
AIR ... we're not quite up to date with the latest Adobe AIR SDK (I think we're on 2.6), but again if there's a demand we can produce an Amethyst that will work with the latest AIR SDK.
On the Mac, we're looking at that and we aim to work (that is, debug and deploy) seamlessly across iMac, iOS and Windows. Clearly, we are fundamentally Visual Studio based and that isn't going to change, so all development will have to be done on Windows via VS. We're not in the business of building core IDEs.