Some questions about buying bonds

Estimate the yield-to-maturity from Jan 01, 2021 as: 100 - 104.061 = -4.061; -4.061 / 9.83 years = -0.4131; Coupon of 4.5 - 0.4131 = 4.0869; 4.0869 / 104.061 = 3.93% .

http://www.kbhscape.com/bond.htm

Expect $22.50, per $1000 bond, paid twice a year but at redemption receive 4.061% less than paid for the bond .

If this is a $1000 bond, do I pay somewhere between $1,000 * 103% = $1,030 and $1,000 * 104.061% = $1040.61?

If you put in a market order, you'd pay the asking price (104.061%) plus any accrued interest since the last coupon. So you'd pay 104.061 plus about 5 months of interest (since it past paid on 7/30) or 1.875 + 104.061 = 105.94

But 4.5%/103 = 4.37%, and 4.5%/104.061 = 4.32%, not 4.116% or 4.123%

Yield to Worst and Yield to Maturity is not that simple. It's an iterative calculation that finds the interest rate where the present value of all future cashflows equals the market price. It's basically the rate that you "earn" on the bond when taking the discount or premium into account. Since you pay a premium for the bond (more than 100%), the yield is slightly less than the coupon rate. Yield to Maturity assumes you hold the bond to Maturity; Yield to Worst calculates all possible yields (taking all possible future calls into account) and gives you the worst yield possible.

Do I get $45 every year (either $22.50 twice, or $11.25 four times)?

Most corporate bonds pay coupons every 6 months, so you'd get $22.50 twice, but check the terms of the bond to be sure. Your bond broker may also tell you what the frequency is.

And $1,000 in October 2030 (unless it's called early)? Is this why the yield is 4.1xx% instead of 4.3x%?

You'd get $1,022.5 since you also get the last coupon, but yes. You also get $1,000 plus any accrued interest if the bond is called. The yield is lower than the coupon because you may more than the face value for the bond, not because of the call.