The IRS does not give extensions to pay your tax due. But you can apply for a payment plan. An extension does not ever give you more time to pay tax due---it only gives you extra time to file your tax documents. You still have to pay by the deadline even when you have an extension for filing.
https://www.irs.gov/payments/online-payment-agreement-application
No. You may pay $1,000 now, but you still have to pay the full amount or apply for installment by filling up form 9465 on or before 4/15/2021 to avoid paying penalty and interest. The IRS allows taxpayer/s to pay the tax liability up to 72 months. You may file Form 4868, Automatic extension to file US individual income tax. If you owe tax, interests continue to accrue until it's paid.