1) It's a historical artefact. When kana spelling was modernised, some things weren't changed. は is only "wa" when it's the particle.
2) Practice, practice, practice! Don't worry, it will improve with time.
3) There are things that contain no kanji, but lack of the right grammar and vocab are what will stop you reading. Children's books are something a lot of people try but they really aren't good for beginners. You do sometimes see "graded readers" meant for Japanese learners but probably the best thing is to get a textbook which will have some reading passages for you.
For just practising katakana you can always try to sound out a few things on Japanese websites. I'm literally talking about just going onto Amazon or googling メニュー (guess what that word is) and seeing how many words you can recognise/work out. Not all katakana words are from English of course, but quite a few will be. Plus a lot of general words on websites - look for ログイン ヘルプ etc.
4) Genki is used by a number of universities and is generally highly regarded. If you've just learnt your kana it would be a good next step.