>It has 1X but it's allowed to lend out upto 10X
No, a bank cannot lend out 10X of it's deposits. That's simply wrong.
Say a person deposits $1. The bank owes the person $1. If the bank thinks this $1 is unlikely to be withdrawn soon, it can lend out $0.90 (assuming a 10% reserve rate). End of story. This bank having received $1 cannot turn around and lend $10. Note that this point the bank has $0.10 of the original persons assets, owes that person $1, and is owed $0.90 by the borrower. The net position of all this is zero for the bank.
Now, the borrower can deposit the borrowed 0.90 (assuming it's not spent somewhere else) into that bank, or some other bank. The process repeats.
The net value to society is zero. Liquidity is added, debts are added, they balance to zero.
If a bank lending money is creation of money, so is all lending. I lend Bob $10, he lends $10 to Fred, he lends $10 to Joe, and since we don't have fractional reserves, this is an infinite multiplier. However the chain of debts and assets still is zero sum. There is no difference between this and banks, except banks are required to hold some cash on hand to handle normal business transactions.
>By controlling the interest rate, the Fed controls and levers the up and down of this huge money supply.
Not quite - a bank will loan any money it has at the highest rate it thinks is profitable (as would any actor in the economy). No bank loans are at the target rate the Fed sets.
The Fed does not control the interest rate, they set the Federal Funds Target Rate, which is a target. They do not lend money at this rate [1]. Nor do banks, except to each other, and only overnight.
Banks lend money to each other overnight to meet reserves, and each pair of banks sets a rate it thinks is worthwhile, like any open market transaction. The weighted average of these loans is the "federal funds effective rate". The Fed wants this number to be the Federal Funds Target Rate, and they use FOMC to buy/sell assets to try and get banks to lend to each other at the target rate. This has almost no effect on the multiplier, since it does not change the reserve requirements, and the usual fluctuations are tiny.
Nowhere does the Fed set a rate and lend at that rate, or even force others to lend at that rate. It's a target.
And no where does this force banks to lend or not lend to others. Banks decide to do this at whatever rate borrowers will pay.
[1] https://en.wikipedia.org/wiki/Federal_funds_rate