1) Everything is Karma - and there is no such thing as a coincidence. All that happens to us is based on our own past actions over previous lives so even if there seemed to have been an opportunity for escape, there wasn't. Before taking birth in these material bodies we agreed to many of these tests that takes place so we accepted these physical bodies to fullfill as per our Karmic debts.
Therefore these questions you ask are difficult to answer, although if there are such countries that are very safe for women to travel in, Norway would certainly be one of them.
B) You mention that you've already visited Oslo, Stavanger and Bergen - in fact you have seen Norway in a nutshell then, and the Western coast of Norway is suposedly supose to be the most beautiful place in all of Norway.
C) To choose between bus, train and plane is an easy option - go for the train. In fact NSB offers something called "Mini pris" which means that if you book well in advance you can take any train journey anywhere in Norway for as little as 199, 299 or 399 NOK one way (for instance from Oslo to Bodø with Bodø being the last train station in the north of Norway). You will pass by Trondheim as you have mentioned, but that is a stop about halfway so you can purchase a Oslo-Trondheim one-way "Minipris/Mini Price" ticket, and then another one from Trondheim to Bodø.
Do try to stick to urban areas and only go out in the wild in tour groups, this is not necessarily due to danger from people, but also weather conditions, lack of transportation etc. Travel in summer.
From Bodø you would have to catch the bus north to Tromsø, and if I am not wrong then it is about a 7 hours journey or so.
D) Have you heard of "Hurtigruten"? It is a transport port ship rather than cruise ship which starts from Bergen, however you could travel from Oslo to Bodø by train, and then purchase a Hurtigruten ticket from Bodø to Tromsø as it has many stops on its way.
E) Norway can be very expensive, with hotel nights ranging from 1000 to 2000 NOK for a fairly normal room ,and since you will pass so many "touristy attractions" then how about just going a few of the places now and the others another time? Obviously you can find hostels in many of the places but still it can be tricky since Northern Norway has no rail network beyond Bodø, and the fact that ferry trips can be pretty pricey.
I visited Norway last year as a tourist with a group and I absolutely loved it. It is the most beautiful country I have ever been to and I have been to quite a few. Breathtaking landscapes. I fell in love! We only visited Stavanger, Bergen and Oslo though.
So this year, I want to go back again and see the places I haven't seen. I basically want to cross the entire country from south to north if that is possible. What is the best way of doing that? Train? Bus? Car rental? I don't want to take the plane. I want to see the places I will pass by. I want to visit Trodheim and Tromso on my way to the North Cape.
I am female and I think I will be travelling alone this time. Will that be ok? How many hours or days will it take me to go from Oslo to the North Cape?
Thank you very much