German confusion, and success with pronunciation

We spent a couple of hours yesterday going through an old German language book, mostly just reading the first 3 exercises. It starts by describing Miesbach, ein Dorf in Deutschland, which has a church, a tree, a street, and a car. Very easy stuff but a real challenge for someone who can't get her tongue around German pronunciation. She's really struggled with the ei and ie sounds, repeatedly swapping them as in English. I think we finally got that one sorted, and I'm really proud of her efforts to correctly pronounce the ch sound, she's now more or less doing it correctly all the time. The other two chapters were a description of a painting of a yacht in the North Sea, and the story of young Liesl and her family.

Very basic stuff. I can happily report that we were both able to read the stories with a good degree of correct pronunciation, and she even understood the gist of them. Words that really confuse her at the moment are auch, segelt, schon and schön, kein and klein, and of course we're both really struggling with getting our head around when to use die, der and das. But at least we know that die and der correspond to female and male, but how do you know if something is male, female or neuter? I mean when you're talking about a tree or a street these things are objects, not people. Anyway, we understand that German will require time and patience to learn, and I guess like Italian and Spanish which also have gender and neuter we'll just have to practice, practice, and practice. If any German speakers have any simple rules that work in the majority of cases that would be awesome.

Other things that confuse us, the difference between traurig and entshuldugung, which do we use, and in what context, the phrase books don't explain. Both books define them as 'sorry' or 'apology'. In English these words mean the same thing but are used in different contexts, 'I apologised to..' or 'sorry I hurt your feelings...'

EDIT: After several months living in Germany, we now know that traurig is much less common, in fact it seems to be used to express sadness, whereas entshuldugung is used in much the same way as we would say excuse me, and if ou actually want to say sorry about something, you would say 'Es tut mir leid', or often shortened to just 'tut mir leid'.