I was in the process of writing several comments all over the place, and realised it would be better structured to put them together as an answer. I answer specifically questions 3. and 4. of your question.
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"3. I have a great interest in physics, but I'm not really much interested in doing experiments: Would it be advisable to do my bachelor in mathematics and try to get into theoretical physics later on?"
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Firstly, my response to some of the answers above encouraging you do a physics degree, including the accpetd answer by ptomato, is do not listen!
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I realise that it may be hard to do before you've even gotten an undergraduate degree, but if you can try to decide which area of theoretical physics you think you might like to work in, it would help you greatly to decide how to specalise your undergraduate degree.
By that I mean that theoretical physics is a large area of research these days. I have some friends who switched into mathematics to go on to become string theorists, black hole physicists, cosmologists, particle theorists, quantum information researchers etc. as well as fields outside of theoretical phyiscs like meteorology, many kinds of maths biology (from cancer to nuroscience to informatics), genomics etc. On the other hand, some, such as myself, stayed with physics to go on and become cosmologists, astrophysicists, computational physicists, geophysicists, complex systems physicists etc. all doing theoretical work.
(I should say that we are only at PhD student age now, not university lecturers or anything like that, but this gives you an idea of the many fields that you can go into).
What you'll notice is that absolutely none of us went into condensed matter physics, a very large area of theoretical physics. And this is why I highlight ptomato's answer as terrible terrible advice; If you fore people to do things again and again that they are not enjoying, they will more likely learn to resent it, than grow to love it! His claim that
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"These students run into trouble when they're looking for internships or final projects, because no professor will accept them"
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is pure and utter rubbish, again, in my humble opinion, which is based on the experience of my fellow class-mates. In fact, I vividly remember one physics lecturer saying that he prefers to take on the maths-physics students for PhD research. Using a metric of "number of students who went on to further research", the maths-physics degree had the highest number, by a long shot!
The university I went to is quite big in condensed matter physics, and there was always a high focus on this in our lectures and labs (labs were compulsory in all years. We had no choice in our lecture courses. I believe this is not common in some other countries, so maybe it is not a worry for you?). Many of us did not like it, which resulted in over half switching into pure maths. The only reason I did not was because I was stubborn, proud and arragont (which, as a side piece of advice, don't be stubborn, or overly proud etc. I can tell you, you won't get anything out of it, and will loose a year playing catch-up to your more humble maths-physicists friends who took the leap!).
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From the sounds of your comments, it is obvious that you really like maths. So why not do a maths-physics degree? That way you'll see both sides, learn lots of interesting things from both departments, and keep your options open.
I just repeat that doing a straight physics degree, in my opinion, given that you want to become a theoretical physicists, would be a very bad idea.
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4.Is there a real chance of getting into research afterwards? (not that any kind of answer to this question would ever stop me from trying...)
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For your second question, again, I can only offer an answer from the point of view of a current graduate student.
To start, that attitude is definitely the right sort of one to have! People will tell you that it's very hard, which it is, and that you'll need a bit of luck, which you will, but most of all, you need to not give up before you've even begun!
As far as how likely it is to get into research, again, for starters, it depends on what you want to do. I have friends who switched into maths biology, and money is thrown at them. Others who want to be string theorists and algebraic geometrs, not so much!
Moreover, it depends on your country. I come from a country with very little funding in fundamental physics (theoretical particle physics, string theory, maths-physics etc.). Most of the funding goes to materials physics, experimental physics, computational physics etc.
I now like in a country with more funding for maths-physics, which is great, but they are a little hostile to forigners, and funding for foreign PhD students and post-doc researchers is far harder to get than for nationals. But there is still some money out there, so it's not too bad.
In other countries, the US, Netherlands, Germany mainly, there is lots of funding, if you're good, and most PhD students once accepted get funding, and post-doc researchers even get a good wage (relative to where I am now, in case that angers anyone!).
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For now, my advice would be to hold on to your ambition, and work hard at your undergraduate degree. Assumedly you have several years before you need to think about these things.
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And with that, I wish you the best of luck!
