Here's my two cents.
Would the IRS assume that the income was evenly earned throughout the year?
Yes. However, there are forms (included in the TurboTax program) that allow you to specify your business income/expenses for each quarter, and that can reduce or in some cases totally eliminate the late payment penalties. For example, if you opened your business in the 2nd quarter of the year, the IRS will assume otherwise and the program may figure a non-payment penalty for the first quarter. But using options in the program you can indicate that you made 0$ income in the first quarter, and the penalty for that quarter would just "go away". I'm not getting into the program details of that right now, because those details flat out do not matter until you actually start your 2020 tax return, next year.
(I found that the IRS website has a long, complicated document and worksheet on figuring this out,
In my personal opinion, (and we all know what those are like!) don't waste your time with those worksheets. But you most certainly can if you like inducing self inflicted permanent brain damage. 🙂 I've been self-employed for over 15 years now. What I do is send the IRS 20% of my *GROSS* business income each quarter. Then at tax filing time I am "always" well within $1000 of my total tax liability. The IRS rules are, if what you owe at tax filing time is more than $1000 or more than 10% of your total tax liability, whichever is *HIGHER*, then an underpayment penalty will be assessed.
With my self-imposed 20% rule, I have always been within $500 of my tax liability with only two years where I owed the IRS, instead of getting a refund. Of those two years I owed, the highest I owed was $472. Not an issue. I just wrote the check payable to United States Treasury and called it good. So did the IRS. No penalties, late fees, interest or anything of the such.
Would I owe estimated taxes for 2020?
If your business has W-2 employees, then you are "required" to submit payroll taxes to the IRS at least quarterly, and if the wages are high enough it could be required monthly. Same holds true for your state, if your state taxes personal income. State taxes are completely separate from federal taxes, so you can not pay state taxes at "ANY" irs.gov website.
As for estmiated taxes on "your" business income, if you don't pay estimated taxes and at tax filing time what you owe is over the thresholds mentioned above, then yes you need to pay estimated taxes. The sooner you pay those taxes for the quarters you're late on, the better. You can pay the IRS "right now" if you want, at www.irs.gov/payments. Pay attention to details on that website so that you pay for the correct tax year. If you pay for the wrong year or wrong quarter, there is "NO" "POSSIBLE" "WAY" to fix it.
I would also like to know about the penalty relief waiver mentioned here, and whether I would qualify.
I don't see why you wouldn't qualify, provided to pay your "catchup" quarterly taxes as soon as feasibly possible. But understand that the IRS can only waive penalites and fines. The IRS can not and will not waive any interest, because the law (i.e.; Congress, who made the law) says they can't. So the sooner you pay past due quarterly payments, the better.
