Question 1: How can I make my internal strength useful against unwilling (or more likely free willing) opponents that are not constrained to the traditions of my chosen system? Question 2: Is the ability to change structured knowledge into free-form usable skill something that can and should be taught to you or is it the responsibility of the student?
The first thing, of course, is to find and develop such strength. There is a lot of talk about "internal" strength but very little clarity. Clarity regarding what it is you're trying to develop is necessary for its development. We use "intrinsic strength" yet this isn't necessarily what you mean by internal strength.
In any case, power, regardless of form, is not the main factor--skill is. Handling unwilling partners is a complex matter and you need to develop the skill and understanding necessary to do so. It isn't a matter of just having some form of power, although a healthy degree of power is necessary. As Ku Yu Cheong (greatest "iron palm" master -- able to break thirteen large stone bricks at once, all resting flat on a slab) said to a man who demonstrated he could break five: "That's good, but now try to use it against me." The man couldn't and Ku pointed out that power alone is worthless without boxing skill.
To interact effectively with an unwilling opponent, one must first fully acknowledge his unwillingness, which from his point of view is merely the desire to win, and you should remember: that's his job! He's doing what in his mind is appropriate. Let it be that way and join it, don't fight it or resist it. Use what he is doing against him. This of course requires skill, and therefore proper training. It is not done simply by having the idea--you must take this idea into effective action. Once again, this is not something that can be accomplished by reading about it.
Both. It must be taught by someone who understands what it is, but it must also be taken on by the student -- researched, contemplated, tried out, etc.. As you play with people, commit yourself to working on some principle such as staying relaxed, using the whole body, moving from the center, joining, etc. whether you win or lose, and see what you discover. It is of much greater value to investigate these principles than to concentrate on winning or losing. But like I said, you will gain so much by some hands on work with us here. It will make a 100% difference in your practice and play.
Good luck, hope to see you in the near future.