1. you answered your own question there. If the I/C pump was out, it would run like a turtle on depressants. ( and unless you are totally deaf, you can hear the blower whine )
2. Go for a AGM battery. I personally like this one : Intimidator 9A48 Group Size 48 (H6) AGM Battery - Remy Battery
3. Don't want to weigh in on this, too many different opinions - use search.
4. yes, unless you are a purist then get Bosch replacements.

Welcome to the forum !!!