Also, I welcome any criticisms of my process as I have described. I am new to homebrewing and I welcome any advice. I will not be offended. Thanks.
There's a lot to unpack here. So please don't be taken aback if I address lots of this in pieces.
I recently brewed an Oktoberfest German lager. Now, criticize me all you want but I used liquid California ale yeast to ferment it. It was the only yeast I had on hand and I fermented it at around 70F (ambient temperature) so I know technically it is not a lager.
You made an amber ale. There's nothing at all wrong with that. Just just call it what it is.
This was my first all-grain brew and I did not account for sparge water evaporation during heating. I ended up with closer to 3.8 gallons of wort instead of my intended 5 gallons. My original gravity ended up being 1.069 (too high I am aware). I just didn't want to add tap water to my wort.
Heating sparge water up to sparge temp didn't result in the evaporation of 1.2 gallons of water. Perhaps you mean you boiled away more than you planned/expected during the actual boil? Also, how did you determine the total water needed? Here's the total amount water you should need for any given batch:
Desired batch size into the fermenter
+ grain absorption
+ unrecoverable mash tun dead space
+ tun to kettle transfer losses
+ kettle hop/trub absorption
+ boil off
+ kettle to fermenter transfer losses.
Some of the above may not be applicable, depending on your equipment and process. Are you using brewing software? If so, be sure to tweak its parameters to match your equipment/process.
I decided to move the beer into another plastic bucket and place it in the fridge overnight. Tomorrow I plan to begin bottle conditioning. A question I have: is cold crashing worth it?
There was really no need to move the beer to another bucket. And that exposes the beer to more oxygen, which is generally not a good thing. In general, you only want to add oxygen when you are pitching the yeast, before fermentation.
A question I have: is cold crashing worth it?
Cold crashing can definitely help clarify beer, and can be worth it if clear beer is important to you. But cold crashing reduces pressure inside the fermenter, and unless you have a way to prevent oxygen from being sucked into the fermenter during the crash, I would recommend not doing it. (A standard airlock won't prevent O2 being sucked in.)
I was wondering if cold crashing drops enough yeast out of solution to affect my bottle conditioning time.
I suppose it could affect conditioning time a little. The usual question is "will there be enough yeast left in the beer to bottle condition?" And the answer to that is "almost always." It's very hard to remove all of the yeast. Only filtering (or perhaps centrifuging) can do that. People have lagered beers for weeks or months and then bottle conditioned without issues.
Congrats on your first all grain beer!