papi, don't worry.
Sounds like you have a few tricks to learn yet, but they will come with time.
As for sanitizing, yes you ought to buy one of the many true sanitizers out there and use them exclusively. But you are probably OK for this batch. Just remember, nothing will grow in there that will kill you. ...I think. So don't worry.
There is something wacky about your initial reading, for sure. Did you say you filled the tube it comes in and floated it in THAT? Mebbe I read that wrong, and for all I know that is what you are supposed to do but me, I take the easy way out. I keep a bucket by me with sanitizer in it, and keep a few things soaking in it. The hydrometer is one of them. Then I float that sucker directly in the bucket once it is chilled. Maybe not the prettiest way to go, but it works for me. For you? Relax, don't worry.
When I brewed my first batch (recently, by the way), I made at least a half dozen mistakes that were so amazingly stupid each of them was worth 25 floggings with a wet noodle. The biggest offense was indefensible... I fermented in the bottling bucket. (In my defense, ahem, I brewed 25 years ago and there was no "bottling bucket" with a spigot. I saw this and thought, 'oh, how cool, I don't have to siphon...' Long story short, I fermented that batch in my office [wood floors, oriental rug] and when I was getting ready to put it in bottles I must have tapped the spigot with my foot and opened it a bit. Three hours later when I walked in to grab it, it was 2/3 empty! The rug was saturated, the office smelled heavenly, and my wife was coming home in 30 minutes.
In the end, I still had 9 bombers in that batch that were damn tasty! And I learned several lessons that batch - critical points that I will never have issues with again. So far every batch since has been darn near perfect.
Here's to your first batch, I hope it is tasty! And no matter what, I know your second will be even better.
Cheers-