According to this article, instead of making quarterly estimated tax payments for freelance work I do on the side, it may be possible to simply increase my tax withholding at my full-time job. I expect that I will owe FICA taxes on at least some portion of my freelance income. Would increasing my withholding cover those taxes? If not, what is the best (i.e. most convenient + legal) way to approach this assuming I am maintaining a full-time job as well as some freelance independent work (1099)?
Technically you owe 'self-employment' taxes not FICA taxes because they are imposed under a different law, SECA. However, since SE taxes are by design exactly the same rates as combining the two halves of FICA (employer and employee) it is quite reasonable to treat them as equivalent.
SE taxes (and income tax also) are based on your net self-employment income, after deducting business expenses (but not non-business items like your home mortgage, dependent exemptions, etc which factor only into income tax).
You owe SE Medicare tax 2.9% on all your SE net income (unless it is under $400) adjusted down by 7.65% to compensate for the fact that the employer half of FICA is excluded from gross income before the employee half is computed. You owe SE Social Security tax 12.4% on your adjusted SE net income unless and until the total income subject to FICA+SECA, i.e. your W-2 wages plus your adjusted SE net income, exceeds a cap that varies with inflation and is $127,200 for 2017. OTOH if FICA+SECA income exceeds $200k single or $250k joint you owe Additional Medicare tax 0.9% on the excess; if your W-2 income (alone) exceeds this limit your employer should withhold for it. However the Additional Medicare tax is part of 'Obamacare' (PPACA) which the new President and Republican majorities have said they will 'repeal and replace'; whether any such replacement will affect this for TY 2017 is at best uncertain at this point.
Yes SE taxes are added to income tax on your 1040 with schedule SE attached (and schedule C/CEZ, E, F as applicable to your business) (virtually so if you file electronically) and paid together. You are supposed to pay at least 90% during the year by having withholding increased on your W-2 job, or by making 'quarterly' estimated payments (IRS quarters are not exactly quarters, but close), or any combination. But if this is your first year (which you don't say, but someone who had gone through this before probably wouldn't ask) you may get away with not paying during the year as normally required; specifically, if your W-2 withholding is not enough to cover your increased taxes for this year (because of the additional income and SE taxes) but it is enough to cover your tax for the previous year and your AGI that year wasn't over $150k, then there is a 'safe harbor' and you won't owe any form-2210 penalty -- although you must keep enough money on hand to pay the tax by April 15. But for your second year and onwards, your previous year now includes SE amounts and this doesn't help.