"1. There are not any UCAVs (unmanned combat aerial vehicle) currently deployed that have capabilities close to those of current-generation fighter aircraft. That is being worked on, though not at the level I would like to see.
Current generation drones are (as far as I am aware) designed to be piloted remotely, and aren't really designed to shoot down other aircraft."
Right. There has been discussion of a drone version of the F-35. I couldn't find much recent discussion, which probably means it's now behind the veil of classification. One thing to remember is that as you need more speed, range, and payload that will be directly reflected in the size of the aircraft. Small drones can't carry a lot of weapons, fly particularly fast, or very far.
http://www.washingtonpost.com/wp-dyn/content/article/2006/08...
I read an interesting article fairly recently where Russian ideas for unmanned fighter aircraft were discussed - the approach there looks to be manned "leader" aircraft directing larger numbers of unmanned drones. This is probably how the West will go as well, since it's important to have local C&C in case communication systems are compromised. It also at least gives the appearance of "human in the loop" rather than fully autonomous lethal operations.
"2. With missiles that can strike an enemy from beyond visual range [1], it is often argued that dogfighting is no longer important. Current generation missiles are supposed to be pretty good."
While this is all highly classified, it's unlikely that any adversary's long-range radar guided missiles will work against the F-22 or F-35 (or B-2 for that matter) at anything like their maximum range. A guess would be that if the missile had a max range of 100 miles against a Gen4 target, it would have an effective range of 10 miles or less against a Gen5 target.
The Achilles heel of stealth aircraft is IR detection. There is no getting around the laws of thermodynamics and waste heat. There are some mitigations that help, such as rectangular cross section engine exhausts, but LWIR missiles detect the thermal radiation from the rigid body (hardbody) of the aircraft and home in on that.
Note the mention of the "backup" IR sensor (BTW the described system is quite interesting in other ways):
http://www.popsci.com/china-new-long-range-air-to-air-missil...
It is worth noting that having a high-quality IR sensor on a hypersonic missile is a very tough problem due to heating.
"3. There are degrees of stealth, and improvements to detection systems also continue. As far as missiles go, people have generally had a hard time shooting down stealth aircraft, though it is possible."
If you're able to locate the stealth aircraft in time, IR missiles can be effective. The problem is that it's likely the first realization you'll have a stealth aircraft is around is when it launches a missile at you. One virtue of sensor fusion and networked aircraft is that aircraft further back (including AWACS) can use radar, then deliver targeting information to aircraft closer to the enemy. The F-35 can also cue weapons from other platforms - recently there was a successful test where an F-35 successfully guided a Navy SM-6 SAM against an air target. The SM-6 has over a 200 mile range...
http://nationalinterest.org/blog/the-buzz/lockheed-martins-f...