#1, yes you could possibly be assessed a penalty, depending on the amount of tax due and how much tax you paid last year.
#2, yes, even though you make a timely estimated payment, if the estimated payment is still significantly under what you owe, you could be assessed a penalty.
The payment deadline for income earned from Sept 1--Dec 31 is January 15, or January 31 but only if you file your return by January 31 and pay in full at that time.
You can avoid an underpayment or late payment penalty as long as the amount you owe when you file your return is less than $1000, or the amount you pay to the IRS during 2020 (by withholding and estimated payments) is at least 100% of your tax bill from last year (or 110% of last year's tax bill for certain high income taxpayers).
Estimated payments owed for 2021 are based on your 2021 income. Turbotax will give you a figure using 2020 income but in your complicated situation, it will provably be inaccurate. Your first 2021 estimated payment will be due April 15, for income paid between Jan 1-March 31.
