I'm very sorry you're going through this; dental pain can certainly be unbearable when severe.
I'm not in Germany, but the US, so there's a good chance my reply may not be helpful at all, but since no once else has responded up to now I thought I'd try.
1) A general dentist would and should not do root canals, or I suppose they might attempt it, but I don't think I would trust the outcome. You need an endodontist; your dentist should have made recommendations to you. Endodontist are specialist in the root pulp of the tooth and are specialist in root canal work.
2) 700 euros for two root canals sound awfully inexpensive to me. (Right now the conversion rate is about 1€ = $1.) I would expect to pay that for one root canal in a smallish town (15,000 population). In a larger city I would expect that it could range from $800 to $950 US dollars per tooth. Not saying the price necessarily reflects the quality of work (dunno... Are dentist not well paid in Germany? Are they more middle class, lower-middle class?), but the relatively low price would be a tip-off to me.
3) My honest opinion is that I would forget about this dental practice altogether regarding repairing the botched job. I wouldn't even go to another dentist within the same practice since they may all function under the same general skill level/philosophy of work ethic. The theory "water seeks its own level" applies to a lot of things in life.
(btw: in the US this practice of "doctor-hopping" within a practice when dissatisfied generally is not allowed. It has to do with medical professionals sticking together -perhaps because of liability/malpractice/lawsuit risks- and also not wanting to step on one another's toes and not wanting to be the corrector of a co-worker/colleague's work)
I realize you've paid for this bad dental work with your hard-earned money, but your first priority should be to get in with a highly recommended endodontist and get the dental issues taken care of now. You don't want infection, pain or any kind of problems that down the road only become bigger, more expensive problems. I'm honestly not sure what your financial recourse would be, but you only get one set of adult teeth and you want them to last your entire lifetime.
I hope someone on here can make a recommendation for an endodontist for you in the Berlin area.
Good luck to you,