I have always loved norse mythology, but accessibility to the stories undiluted by modern interpretation, or secondhand have been far and few.
So less one question but a couple:
Sorry for late response.
As for Old Norse myths and OP's first two questions, I'd recommend to the book on the what medieval texts actually say rather than some (often dubious) modern 'rational' interpretation at first. From this point of view, my first recommendation would be: John Lindow, Norse Mythology: A Guide to the Gods, Heroes, Rituals, and Beliefs, Oxford: OUP, 2001, meticulously referring to the primary texts that mention deities and heroes in question. Read entries while also sometimes checking the actual texts of the translated Eddic poetry together.
On the other hand, it would also be very handy if you know more about why medieval Icelanders, such as Snorri Sturluson, decided to record some mythological episodes in parchments more than two centuries after the alleged official acceptance of Christianity in Iceland, and how they regarded and understood these episodes, since we have only access to almost every existent written evidence on the Old Norse world view by way of their writing.
On the Runes, Michael P. Barns, Runes: A Handbook, Woodbridge: Boydell, 2012, is probably the most balanced overview of the runes and their use in Scandinavian society from pre-Viking Age mainly down to the Reformation, at least in English. If you are interested more in the introductory reading, however, to check your nearby libraries to find the copy of the classic of this field, Ray I. Page, Runes (Reading the past series), London: British Museum, 1987, might serve your purpose better.