I've decided that in order to preserve my sanity I need to find a part-time personal assistant. I'm not sure that is the appropriate title but this person would need to be ready, willing and able to assist with a multitude of tasks like housekeeping, research, pets/vet visits, childcare, homework help, meals, shopping and other errands as necessary. My question is where in the world do I find someone that would be interested in very part-time work of that nature and what do you think is a fair hourly rate?

So...you need...a wife? LOL! That's what I always say, but my feminist alter ego corrects me that the correct term is "domestic assistant".
I would use the classifieds (or craigslist) both ways...find people looking for housecleaning or childcare work and interview them to see if they are suitable. Prepare a list of all the duties you expect to be done (or hours you need help), post a job listing and see what happens. I gave applicants a list of tasks and told them I could do the list in three hours, and I would pay up to $60 a day to have the tasks completed, or $15/hr, "whichever came first"...
I pay our household helper $15/hr, and she is worth every penny, recently I gave her a raise to $17.50 (after 6 months of excellent service). I don't have to pick up or de-clutter when she comes, she knows our family well enough now to incorporate that into her cleaning/organizing.

I know that if you have a Cleaning Service come out to your house and tell then what you are looking for that these people would like that extra service on the side! I own a cleaning company, but we do A Lot more than just clean we do errands, such as: grocery shopping, vet visits, meal cooking, laundry service, running kids to there activities...etc... If you ask we always work it in! But you have to find a small business owned company. Marry Maids will not do all that! Post an add on Craigs list!

I've heard of personal concierge services. Here's a link to one in my area: http://www.personalconciergeseattle.com/. It might be a lot pricier than a college student, but it might be at least worth looking into!

Your wish list is pretty varied and long, so you might need to narrow it down in order to find someone that's good at 2-3 things that you really need and/or REALLY don't want to do yourself.
Several of the tasks are in the nanny-realm, so a personal assistant might not be what you're actually looking for. However, if your need is heavier on the errands and research end, you might be looking for a personal assistant.
Are there any occasional sitters you use that might be interested? Local colleges or sitting services would be a good place to start. Ask around, too. Oddly enough, my SIL was talking to someone in a park when they came to visit us here and ended up with the number of a "Go-to-Girl" service, that does all kinds of errands and tasks, similar to what you're looking for, but I don't know where I would have gotten that number without that random interaction. I would probably look to pay the same as the going hourly rate for a nanny/sitter. Plus, you'll need to pay gas if they use their own car for errands.