Are these good reasons for starting a new PhD project? If have just finished the first year of my PhD studies in mathematics at a German university. After my master's, which I have done in representation theory, I had started a PhD in a more applied field, partly because my current supervisor pointed to the necessity for knowledge in representation theory in his field. However, I have been feeling disappointed since almost the beginning. The reasons are as follows:


For the problems I work on, my supervisor can barely act as an advisor. He has almost no expertise in what he asks me to do. If I talk to him about a point where I have no clue how to proceed, I have to explain basic material to him instead of obtaining useful hints.
He is unwilling or unable to provide me with suggestions on what to try, whom to ask, what to read etc. Probably, I should be able to do all these things on my own. In the case that the expectation is that I should state my research questions, find helpful material, and solve them completely without any advise, I am suspecting that I am not apt for pursuing a PhD.
There is also no vivid exchange between me and the other PhD students. This is mostly due to the fact that my supervisor has hired students from completely different backgrounds to work on very unrelated problems, which only have in common that he is no expert in any of the fields he has hired students from. However, when talking to my colleagues, it seems that I am the only one suffering from this isolation.
It is hard for me to spot and solve problems completely on my own. When starting my PhD, I had hoped for an opportunity to learn new things. Until now, I haven't learned anything. That I have my background in a different field does not make things easier, but I think that I would also struggle in my original field if I constantly have no one to talk to.
The social climate in the group is quite cold, also apart from talking about mathematics. Again, my colleagues seem to be fine with this solitude. This is fine, and, to be honest, I actually envy them for not needing exchange, company or just some chatting about what they do. I have the impression that I cannot live that way, which more and more seems like a deficiency to me.


These are the reasons why I have applied for two opened PhD positions I have found in January, both in representation theory. Contrary to my expectations, both have offered me the position. However, I hesitate to accept one of these positions because:


How can I be certain that I am good enough for these positions? Yes, they have judged my application, based on a talk I gave there and based on what I wrote in my master's thesis, they are experienced professors, but how can I be certain that I am good, creative, persevering etc. enough?
How can I be certain that the reason for my distress is not my working group, professor etc., but my lack of aptitude for doing a PhD? Shouldn't I be able to work independently, without the need for talking to others about what I do? Shouldn't I know of my own which questions I want and can work on?
How can I be certain that I will feel better if I start a new project?


Apart from these work-related questions, other aspects that make me hesitate are:


If I quit, I will be 31 or 32 when I finish the new project.
Exchanging a PhD on applied questions from a well-known university for a purely abstract PhD at some less-known university does not sound like a good thing to do with your CV.
For a PhD, the salary and other benefits I obtain know are perfect. This could not be any better and would certainly degrade if I quit.
Arriving in a new town, getting to know new people etc. has always put a lot of pressure on me. It has always taken me monthsto get to make new friends  after having moved to somewhere else.


I am aware that I should try not to take these aspects into account, but I have mentioned them for completeness.

Question: How can I take a good decision?
There are dozens of parameters that seem to be influencing this decision. I will try to touch on a few points as best as I am able:


Coming up with a PhD topic is hard for a lot of PhD students. This is a common feeling; it does not mean you cannot succeed as a PhD student. 
How does representation theory relate to your current subject? Are there papers connecting the two subjects? If so, what do they say? If not, can you discover a link between the two subjects (representation theory and applied?) Your advisor seems to think there is a link. What is that link? (These are questions I would be asking myself as a way to try and discover a dissertation direction).
Graduate students are sometimes distant with one another. They all have their own projects to be doing. That's the reality. I would look for social connections outside of your department if necessary. 
It may be easier to change advisors internally, if possible, than switching universities. Being from the US, I have no idea how feasible this is in your case. 
In my opinion, passion for your subject is overrated as a PhD student. Graduate students I have advised are rarely deeply passionate about our research. But they realize that it is 4-5 years of learning and thinking about a subject in order to develop the ability to perform independent research.
I work at a national lab in the US now. No one cares about the topic of my PhD (probability theory). My master's degree was in representation theory. I never use these topics in my current work. But I've proven that I can think about math and statistics, and I use these skills in my job now as a researcher. I do not know your goals (academia or industry), but industry usually only cares if you have a PhD in a generally relevant field and if you can program. It is that binary.  
Being in your early 30s when you finish a PhD is somewhat normal. There is nothing magical about being 27 and having a PhD. It just means that you have to start going to a full time job earlier in life. If your finances are in okay shape, finishing a PhD at 32 is not the end of the world. 
We speak of a PhD being able to do "independent research." This does not mean you never need help or collaboration. I have a PhD. I collaborate with other researchers. Sometimes I come up with an idea, sometimes they do. And some of their ideas blow my mind--I would never have thought of them in a millions years. 
Being honest, it sounds like your advisor may not be the best advisor on the planet. At least not for your case. Some students really like a hands off advisor, some do not. Both types of PhD students exist and both are successful. Changing universities to get to a better advisor position may not be as huge of a deal as you think. It might actually make your work more enjoyable.