Lot of questions, but I'll do my best.
Then I did a little searching online and started seeing coins being offered for closer to what the stock market was saying silver was worth that day (I think that is what is called "spot"?).
The stock indexes are usually either inaccurate or heavily delayed, kitco.com and kitcosilver.com are my goto sites for everything PM related.
$44.56 including taxes and s/h/ins. So it ended up costing me MORE than silver's daily value
That's 100% normal. You would be extremely lucky to ever get an ASE at spot price, like, stupid lucky. ASEs have higher premiums attached to them due to the fact beyond being a bullion coin they are arguably the most collected coin in the world.
But then I discovered that the $1 Silver Eagle is NOT considered a circulating coin! It is legal tender, but falls under the category of bullion
NCLT. Non-circulating Legal Tender. Think of it as the Kennedy half dollar
nowadays. They still make them, they are legal tender but aren't a circulating coin per se.
My coin has no mint marks, is not a proof, and not grade-worthy. Sure, I intended to get one just for the silver content, but had I made a huge mistake affecting any desire I may have in the future to sell it? It seems that there is no "market" for my bottom-of-the-barrel coin.
Not sure why you think that. Almost all ASEs are produced at Philadelphia, that can be found with a quick search, proofs are much more scarce in terms of number produced and have much higher premiums, and no modern ASE is really grade worthy. As for it being detrimental to future salability and marketability it makes little difference. Your coin as of now is worth spot plus a premium, what that premium is changes in relative proportion to spot. That ratio will likely not change within your lifetime.
How do I know where was my coin minted?
Will it ever go up in value if left as-is?
Nobody can tell the future
Are 100 year old gold coins also considered bullion? They always have value. will mine only be worth the value of its silver?
Sometimes they are, sometimes they aren't. They always have value because they're gold, your ASE will always have value because its silver.
Are mint-marked uncirculated versions that much nicer in quality?
Not at all
As an added aside, I am seeing listings for "emergency" 2020 silver eagles. they only way to know that is what they are is if they are taken from original marked packaging. Who's to say that is what they really are? Doesn't that mean an unopened box of coins has to be submitted to the grading company? Boxes can be resealed, you know. And why do these carry a premium, because a different mint had to take over for a short time? Isn't it still the same boring coin as mine?
There is no difference, it's a marketing gimmick.