Help Needed: Critique my first brew day

[WhiteDelicious]

I decided to brew my first beer. I had spent too much pouring over this forum and others, and i was getting anxious to start. There's still a ton of information that I haven't had the change to read or understand, but I figured the best way to learn was to just jump in. It went generally well, with a few fumbles thrown in the mix. I'm looking for any and all advice for moving forward, and I'm hoping maybe this post can allow some other new brewers to learn from some of my mistakes.

Equipment:
I bought all the equipment necessary to brew 2-3 gallon BIAB batches. I went with this size due to limited space, inability to drink 5 gallons of beer, and experimentation purposes. My goal is to brew smaller batches more frequently, with slight tweaks in the recipe or process, until I really find a method that works well and produces consistently good beer.
-Two 3 gallon glass carboys
-5 gallon stainless steel kettle
-2 gallon stainless steel kettle
-Standard equipment for all brewing (siphon, stoppers, airlocks, thermometer etc.)

Recipe:
I used EdWort's "Bee Cave Brewery Bavarian Hefeweizen"
I believe Ed used red wheat, but I chose to do pale. I cut the recipe in half to make a 2.75 gallon batch, then removed the rice hulls and added an extra 0.5# of German pale wheat (because I could't buy 3.5# from Northern Brewer).

Modified Recipe
------------------------
Recipe Type: All Grain BIAB
Yeast: Wyeast Weihenstaphen 3068
Yeast Starter: No
Batch Size 2.75 gal
Boil Size: 3.75 gal
Estimated OG: 1.051
Estimated Color: 3.5 SRM
Estimated IBU: 14.5

 

[WhiteDelicious]

Modified Recipe
------------------------
Recipe Type: All Grain BIAB
Yeast: Wyeast Weihenstaphen 3068
Yeast Starter: No
Batch Size 2.75 gal
Boil Size: 3.75 gal
Estimated OG: 1.051
Estimated Color: 3.5 SRM
Estimated IBU: 14.5
Mash Time: 90 minutes
Boil: 60 minutes
0.75 Hallertau @ 45
0.25 Hallertau @15

Mash:
I heated 3 gallons of distilled water to 165-degrees F on my stovetop (gas). I mixed 1 package of accumash (will not use again, I just don't have a firm grasp on water chemistry apart from looking at my city water report) into the grain and stirred into the mash.
Mash temp: 154-degrees F. I covered the kettle in a sleeping bag with a heating pad.
30 minutes later, the mash temp was 148. I heated 0.5 gal of water to 160-degrees F and added it to the mash. This brought mash temp to 149.
30 minutes after that the mash temp was 146. I added 1.25 gal of water to 165-degrees F and added it to the mash, bringing the temperature to 150.
After the full 90 minutes, I brought the kettle to the stove and heated to 170 for a 10 minute mashout.
At This point, I removed the bag of grains and dunk sparged them into 1 gallon of 165-degree water. I squeezed the bag, sparged with the hot water, and repeated until I couldn't squeeze anymore wort from the grains.
I checked my pre-boil OG, and it was around 1.041.

Boil:
I kept the wort split between the two pots and brought them each to a boil.
Hop additions at 45 and 15.

Cooling:
I filled my sink with cold water and ice to cool the kettles.
I used a large plastic spoon to stir the wort in the kettles. After each stir, I would clean and re-sanitize the spoon. (This may have been unnecessary or a potential infection risk. I'm not entirely sure).
During cooling, about 8 oz of water from the tap and 1 ice cub fell into the cooling wort. (Is this cause for concern?)
It took 40 minutes to cool 3 gallons of wort from boiling to <60-degrees F.

Racking:
I did a whirlpool for several minutes in an attempt to aerate the wort and move the sediment into the middle of the kettle.
Then I racked into the sanitized carboy with an auto siphon.
I pitched the yeast, setup a blow-off tube, and have the carboy sitting in a swamp cooler with an ambient temperature of around 62-degrees.

Is this recipe suitable for a decent hefeweizen? Did I miss the OG by so much because of the low mash temps? I've thought about keeping the kettle on the stove and reheating as necessary, or I've heard of people putting the kettle in the oven to maintain mash temps. Are these good methods?
Moving forward, my plans are to brew this exact batch again, only fixing the issues i ran into today. What else should I adjust to ensure I'm making the best beer possible?

I'm sitting here staring at the carboy waiting for the fermentation. I need to learn how to RDWDAHB.

 

[Hoppy2bmerry]

Pre boil OG can be effected by the crush of the grain, you did make water additions to bring to bring up the mash temp. Considering, it is okay. What was your gravity after the boil? That's the one you need to calculate ABV.

 

[WhiteDelicious]

My post-boil gravity wasn't much lower than the pre-boil, which leads me to believe I did it incorrectly and the measurement is meaningless.

 

[Hoppy2bmerry]

You've probably read about this, but I know I've forgotten myself, when using a hydrometer the instrument is calibrated for temperature, so if you know the temp of you wort when you took the reading you'll know if you need to correct it. If you had a decent boil going it should be higher. Either way you are making beer, and will find your way to getting your processes honed. Here's aren't typically a high ABV beer, so don't worry. When it is done you can relax and have a homebrew.