I think Mike's earlier admonition that just having internal skills doesn't make you a great fighter (Dan and Rob and others have also made some similar comments) is well put. I'm not usually in to talking about the "feats" that this kind of training makes one capable of because I think people spend too much time training to replicate a feat with incomplete understanding of how they have to rewire the body so that the feat "happens".
Having said that, I do want to address some of your points and maybe make a few of my own in addition. I would talk about these skills on a very gross level as "conditioning". Basic cardio condition is so important in martial arts from my perspective that I'm amazed when I visit schools where nobody really breaks a sweat. Having competed in combative sports a good chunk of my youth as well as been in a few altercations as a result of general foolishness and different jobs I've had (not mutually exclusive, either), I feel pretty confident in saying that being in shape can be a huge deciding factor in how well you perform in certain types of combative engagements. So the idea that you can do anything to someone else without effort is a bit laughable to me.
What I will say is that if you spend the right amount of time conditioning your body to automatically respond to different kinds of stresses and stimuli, you can perform feats that "seem" effortless . . but I don't think that's an uncommon result from people that have spent long periods training any specific skills (carpentry, horse wrangling, etc.). Some of the specific skills (based on my beginning understanding of internal training) that can come from IS training are a feeling of much greater physical strength, speed and balance because:
1) You connect the body together to always move as a coordinated unit - this is not based on timing or mystical awareness - it's a conditioned skill so that you automatically are more efficiently using more of your body's gross musculature (and other conditioned stuff) and connective tissue when performing routine tasks.
2) It takes less observable time for you to move and generate power (either as a strike or throw) because you don't need as much of an observable windup or torque to receive, return and generate power and optimizing the use of gravity pulling you down and the ground pushing you up - instead of local muscles you usually would think of in the arms, shoulders, even hips and legs (like in lots of krotty) that are often used instead. This is tricky because lots of folks think they are not using local muscles to drive physical actions when they are (myself included many, many times) and I think it's a major inhibitor to real progress. A much safer assumption in my opinion is to assume that you are using local muscle and as someone shows you how, work more and more on eradicating it in favor of pure and clean power generation.
3) Here's the biggest favor, in my opinion - is how you learn to read and manipulate central equilibrium. There's plenty of traditional views on this but I tend to simplify my thoughts around the basic up/down/right/left/front/back directions to start, then add in the infinite ways to combine them and you can get a sense of how sophisticated it can get. You learn to control it inside yourself and then make an external force part of you, still under your control (the aiki of allowing an attacker's force to defeat them by joining you to them - into one unit - that you still direct) - but it is far from effortless and requires an immense amount of training and conditioning to get anywhere with it. It can most obviously be observed when you push on someone and 1) You feel like you are pushing against solid ground OR (even better in my opinion) 2) You push on someone and as soon as you touch them you feel like your balance is being mucked with (pushing yourself away, feeling crushed down, etc.). In a strictly combative sense, this can help a great deal with absorbing and avoiding strikes, locks, throw attempts, etc.
So, it can be basically body conditioning yourself in such a way that you can hit and throw with greater power, but less overt movement. You can receive and redirect power/techniques/whatever applied unto you more readily and your sense of balance is improved. It's independent of martial arts techniques, it's training a way to "be" (so much so that I sometimes think people that are used to training via copying an external form have a harder time with getting the goods). It doesn't guarantee invincibility, there's limits on every skill it bequeathes, but it is fun and produces results.
It seems like there's a built in intelligence quotient on how far one is going to get with it. It also seems like your ability to be hyper critical and honestly assess yourself and your progress are also going to be major (and potentially limiting) factors in said progress.
These are interesting times, though, because the cat is definitely out of the bag in that a lot of this stuff got missed somewhere (independent of what "style" you do). A lot of people are working on things now and what results they yield will be fun to watch (and participate in). More and more people are meeting and getting together to see who's doing what (and forming conclusions, rightly or wrongly, that hopefully can be openly debated rather than forming factions).
In some ways it's irrevocably tied into what martial art one is doing - even though I think there's a core set body principles that apply no matter what "style" or "system" you're doing. So that can create complications in actually training the basic skills, but I think that's a natural part of the growing pains in this stuff (maybe) becoming wider spread. There's lots of bandwagon hopping and status grabbing, part of the problem being that your rank in aikido or some other art being no indication whatsoever that you have any skill, knowledge or ability in "this stuff" - and I do think it's enough of a game changer that there's some legit concern over how (or if) this will even be incorporated into one's "mainstream" practice.
But like I said, it's interesting times and I'm no expert, teacher, etc. . . just an enthusiastic participant that's been fortunate (through good luck and creating opportunities) to get some exposure and is now trying to work hard (while still having a family, job, life, too, ha).
Probably not what you're looking for in an answer (and damn did I go on a bit), but it's my take on things at present (ever subject to change and re-edumafication).