K before soft vowels (e, i, y, ä, ö): soft, kind of like the 'sh' in 'ship'. Kemi, Kina, kyla, kärlek, köpa. But only when in the first morpheme of a word! So pojke, vilken, etc. are pronounced with hard k.
K before a, o, u, å: hard, like killer, car, cat. E.g., kasta, kolla, kula, kräva.
There aren't many exceptions to this rule. One I can think of is 'kör', where the meaning is different depending on how you pronounce it - with 'sh' it means 'drive', with hard k it means 'choir'.
Except for the beginning of a sentence, you would in general only capitalize proper nouns/names: Sven, Anna, England, Spanien, etc. ("kvinna" is not a proper noun). There are however a whole bunch of exceptions. For example, you don't capitalize the following:
Days, months, public holidays: "måndag", "november", "juldagen" not "Måndag", "November", "Juldagen"
Languages: "engelska" not "Engelska"
Words derived from proper nouns: "amerikansk" not "Amerikansk"