Dear Inger
You have done an excellent job! I really enjoyed reading your essay. First of all, you focus on questions, not on awnsers. And even your proposal are questions. If we are talking about the universe I feel we should always say ''what if?'' instead of ''that´s the way it is''. It could help to treat assumptions as what they are: assumptions. You ask ''How far is it possible for a fairly well-read lay(wo)man like me to understand the problems and stumble stones at the front of research in theoretical physics without being a skilled mathematician?''; Even though I´m not a professional physicist (I´m on my way to become one) I´m impressed by how meaningful your questions are. It seems you´re able to extract the conceptual framework as far as possible without detailed math. Let me now adress some of your points. I have thoughts about your questions on elementary particles and high energy physics, but since I´m far from being an expert on that subject, I won´t take the risk of saying anything.
1.''Can something come of nothing?'' First we should define what do we mean by ''something'', ''come'' and ''nothing''. There is a notion of causal dependence or time flow implicit in this question. But we are not even sure about what time is.
2.''From where does the God particle get its own mass?'' There are some alternatives for mass generation besides the higgs mechanism. I´ve heard of Mario Novello´s work, but I don´t know the details.
3.''How small would the tiniest parts of space-time be? Planck length-time?(...)Have I done some original thinking, or am I simply wrong?''
Loop quantum gravity predicts something similar! From the perimeter institute page: ''Like the quantized energy levels of the hydrogen atom, the admissible values of area are quantized. Volumes of space, as well as its warping and bending, are also quantized. Thus space is not smooth, but rather granular; like atoms of ordinary matter, there are "atoms" of space''
4.''What would the space-time of quantum gravity be like?''
This is the question that motivates me to become a professional physicist. This is really deep. The anwser to this question could be so abstract it would be impossible to express in words, though making perfect sense in a yet unknwon mathematical formalism. But besides mathematical manipulation, conceptual questioning can also be relevant. This is where, as Craig Callender would say, ''physics meets philosophy at the planck scale'' (please see the book with this title). In my essay I´ve proposed that different anwsers to ''what is space?'', ''what is time?'', ''what is motion?'' at the classical level may lead to new physics.
5.''Ever since the mid twenties quantum mechanics has been developed as a
background dependent theory, without regard to the background independence of the general theory of relativity. How come that the background dependence of was not questioned much earlier, as it could have been already in Copenhagen at the time - at least in principle?''
I´m very glad to see this question. It also makes me think very much. The conceptual framework of GR and QM is so different it would inevitably come to a collapse some day, as it did with the problem of quantum gravity.
6. ''Is''shut up and calculat'' the best thing to do?''
I don´t know. It seems to be, since now modern physics has become so abstract that our mundane conceptual reasoning seems impossible to give any help. But whenever the shut up and calculate procedure becomes fruitless, it becomes intereting to find new paths for new physics besides mathematical manipulation. I agree language matters: QFT is based on fields defined on (x,y,z,t). But if Newton had a different conception of what is time, space, etc, then the whole procedure of defining anything on (x,y,z,t) could be seen as wrong. For instance is motion to be conceived in an absolute or relational picture? QM has tight roots with absolute space and time, while GR is intrsically relational. Bue are we restricted to absolute or relational conceptions of motion? This is where maybe language may come and gives us paths for new physics.
Thanks for a very enjoyable essay.
Best Regards
Daniel