Hi there Almaler!
Those pictures were very helpful in assuring that nutrition is your problem.
You asked how I can tell how. Here are a few pointers:
On the third photo, the leaves are pale, with dark green veining. That indicates a lack of iron.
The reddish colored leaves with the dark green veined leaves indicates a lack of phosphorous.
The yellow and brown edges on the leaves indicates a lack of potassium and/or zinc.
I suspect that the reason your buds are growing so strangely is either a shortage of calcium or phosphorous.
You said that you used rose soil to plant your roses in. I am curious what you mean by rose soil? What did it consist of?
When you use chemical fertilizers like the one you are using, and others, you are giving your plant a quick burst of energy, that then burns out until you fertilize it again. None of this fertilizer remains in the soil. Also, the fertilizer you are using is high in nitrogen, which explains why your bushes are so tall and leggy, with lots of leaves.
You are wiser, in the long run, to add organic material to your soil to build up the nutrients your roses need so that they are there whenever they need them, not just when they get a burst of fertilizer. This is why I suggested you make the additions to your soil. You can add these materials all at once if you like, or a little at a time as you can, whatever works the best for you.
You should also give your roses several waterings with the compost, manure or rose tea recipes listed in the Organic Rose thread of this forum. They will do wonders for your roses.
Before adding these soil amendments though, I would suggest raking off your bark mulch. Your reason for doing this was correct, mulching to keep in moisture is a very good idea. You just need to choose a better mulching material, like well rottted manure, mulched leaves, etc.
Your watering system sounds appropriate, roses like a regular deep watering, but don't like to stand in water.
I am sure that you have leaf cutter bees, because of the clean edged, half circle cuts out of some of your leaves. This is a good thing. Leaf cutter bees get rid of other pests for you. If you spray with Neem oil, try not to do it when the bees are around, as you don't want to damage them.
When your buds are bent over like they are in the photos, what happens after that? Do they still bloom? Do they wither and die?
On your forth photo, I notices a bit of powdery mildew. This is the white powdery mildew on the leaves. You should remove any plant material carrying this and destroy it (don't put it in your compost). You can include is in your spray with Neem oil.
When you spray with Neem oil, you should only need to do it once, and then maybe again in a couple of weeks.
But again, I believe most of your problem is nutrition, not pests.
Get that soil built up and give the bushes a few drinks of tea, and you'll be surprised in the change.
I hope I have answered all of the questions you asked, but if not, feel free to keep asking, no need to feel silly - that's what it's all about!
On the whole, you have some pretty good bushes, they just need a little tweeking to get their best performance.
Best of Luck and let me know how it is going, and again, feel free to ask questions!!