First AG Results

My first AG batch is bubbling away in the primary as we speak. It smells delicious and I have no doubt I'll love it (like all my hoppy children), but I screwed up a few things and have a few questions. First the process:
I started with a 100qt cooler fitted with the typical hosebraid filter, 10# of crushed grain and 3.5g of 165F water. This put my mash at 152F. After 60 mins it dropped to ~148F. I then added 1.5g @ 185F for mash out, but that only brought the temp up to 156F. Vorlaufed and drained into the kettle. I then sparged with 3.5g at 170F. I stirred and let it sit for 5 mins before vorlaufing again and draining. My sparge water only brought the temp up to about 158F. As I sparged my pot quickly reached the 6.5g mark and I was forced to close the valve before all the wort was drained. The drain on the cooler is almost 1" above the floor.

The problems that I can identify are as follows:
I left the cooler lid open during the mash out and while boiling the additional 3.5g which caused my sparge water to miss the temp.
I'm using a turker fryer thermometer. It's hard to say how accurate it is and it only has markings for every 5 degrees.
I possibly lost some sugar due to height of drain and not using all the water added.

The main problem is that my OG was about 10 points low. I contribute this to being my first time, but would like to know where the most important improvements could be made.

Sorry about the long post!

Gah, I forgot to mention one point. I didn't think about it beforehand, but my entire house (excluding external faucets) are connected to a water softener. Naturally, since I didn't think about it softened water was used in the mash. I'm not sure what problems this could cause, but considering how some people monitor their ph with an iron fist I'm sure it did something. In this case would it be better to use *shudder* hose water? Or am I running to the grocery store for 5 gallons of spring water?

Boy a 100 qt. cooler is really big. When I add the additional water on the 1st running it is near boiling at 200-205 degrees. This will give you some additonal heat. For the 2nd run I heat the water to 185-190 and I think my grain gets to 163-165 or so. When my kettle gets full I just collect the remaining in another pot and use it to top up every so often so I have enough for 5.5 gallons when finished. I get a lot of evaporation during my boil. I also use a bit of it to get the yeast going before pitching. Grain crush has a bigger effect on efficiency than most things, make sure it is good.

It took me 2-3 times before I felt comfortable with my equipment so you will get better.

Good call catching the excess in another pot. I didn't even think of that and I had a 3g stainless pot sitting right next to it.
As for the cooler...I was in Menards looking at a 52qt coleman cooler for $24.99 and a 100qt rubbermaid cooler that included a mini-cooler (perfect for a six pack) and a thermos (perfect for [insert alcoholic beverage here]) also for $24.99. I figured if I was gonna go big, I may as well go BIG.

First upgrade, a real thermometer. Next batch, keep the lid closed.

I'm sure you are doing as well as most on our first batchs. It'll be the best beer in the world, so far.