Hello

sound like u both have a great plan with slowly incorporating the different events into your training while developing a running base at the beginning. 

keep in touch!

1.how to get rid of side stich?  slow down, breath deeply till gone (this is what helps me)
2.how often to change running shoes?  i have heard 1-2 times per year.  look at your tread.  when almost no tread in any spot then it's time.
3.how much time should I increase running per week?  never go up in any event more than 10% per week.  take a 30-50% decrease in training for a week every month.
4.should I buy any equipment for swim part training (paddles, fins, etc.)?  depends on the length of your first tri and how well u can swim now.  minimum just get the mechanics right and build endurance with decent form.  getting instruction will be your biggest help.  fins/paddles i feel will benefit u most after your swimming mechanics r good and u have about maxed out your speed.
5.any ideas on how to find a pool membership that is cheap?  Y's, health clubs, universities (universites have nice, big pools)
6.should I try to get a used tri bike or a used road bike?  http://www.beginnertriathlete.com/The%20Steves/the%20steves.htm and http://www.beginnertriathlete.com/biking.htm
7.when racing with significant other is it smart to keep same pace or go seperate ways and try to catch/meet up later?
8.Should I stop increasing time/length on running/biking/swimming at a certain point in training?  like #3, make sure u can do the distance come tri time.