1. "More often" would cut down the strictly anabolic response, and
2. yes, lighter weight would also help push those workouts into cardio territory. But I don't think you have to do an insane amount of reps (like going for an extreme burn and exhaustion on the majority of your exercises) to accomplish that. I'm going to say keep the reps below 20 but no less than 12 per set.
By the way, I'm basing this on what I've observed
myself doing that impedes my bulking ambitions -I'm probably not the best person to be giving advice on how
not to bulk, LOL
I'm assuming you really like strength training more than straight-up treadmilling or stair-mastering

In that respect, you don't have to give up the strength training to stem the bulking reaction (besides, I'd never advise anyone to give up strength training, regardless of their goals -it's way too flexible to be considered a specialized activity). If you want to retain the muscle tone and definition without adding much more bulk, consider dropping the compound, holistic exercises like squats, deads, and lunges from your standard menu. Incorporate them every once in a while, but use them sparingly. My leg workouts these days have consisted entirely of squats, deads, lunges, and back extensions, and they are making my butt huge, LOL. If you want to mitigate that effect, you can trade up lunges for leg extensions with light weight for a month. (Take a picture folks, it's not often I condone isolation movements in place of compounds)
3. The only way protein consumption factors into whether you gain a lot of bulk is when you aren't getting enough. I'm guessing that your protein consumption itself isn't the cause of your muscle gains -the
workout type, duration, and intensity is. The protein
enables the muscle gain, but does not
cause it. Cutting back on the protein will cause your body to start catabolizing its own, and that's not good. So no. Don't change your protein consumption, or your fat intake -in fact, don't change anything about the caloric
makeup of your diet. Just consider balancing your total caloric intake vs. expenditure a little closre to maintenance levels...
4. ...by which I mean you should be getting more than maintenance, but not so much that you are downing the 500-1000 extra calories a day that is typical of a mass-building program. If you shift to a heavily cardio-focused workout, you will be a lot hungrier than you would on a moderate-intensity strength training regimen, but since you're focusing more on endurance-type exercises, the "slight surplus" is being burned off instead of stored (or used to build muscle). I'm a firm believer in strength training's ability to use available calories for building mass, but if you aren't causing a strong enough anabolic growth stimulous (and you appear to be, from what you've said) with your workouts, it doesn't matter how many calories you consume, you're not going to bulk. If you aren't gaining muscle with a caloric surplus, then one of two things
must happen, and they are each contingent on the quality of your workouts: a) the surplus will be stored as fat because your workouts are neither anabolic enough, nor aerobic enough to burn it off, or b) the surplus will be burned off because your workouts are more aerobic than anabolic.
In your case, (and this is just the opine-I-own) I think you're bulking because your workouts are too anabolic in nature, and not aerobic enough. A lot of people automatically attach caloric deficit dietary wisdom to "cardio" style workouts, because that is necessary to lose body fat. My point is, aerobic activity (even light "toning" freeweight workouts) are not synonymous with low-calorie dieting. Keep your calories above maintenance levels, and keep your workouts out of the anabolic zone, and you won't get bulky.