Retirement tax questions

You have to follow the ordering rules for Roth withdrawals. Contributions are always withdrawn first.

You say your contributions were "equal or greater than $2000" and you are having a hard time documenting this.  Suppose your contributions were $2500.  Your $12,000 withdrawal MUST be $2500 of contributions and $9500 of earnings.  You can't say "it's $2000 of contribution and I'll leave the other $500 of contributions for later."

Put another way, if you report that your 2020 withdrawal was $2000 of contributions and $10,000 of earnings, then if you have any money left in the account, the IRS will consider it all earnings when you withdraw it later.  You will have shown by your 2020 tax return that all the original contributions were withdrawn.  

Then, if the earnings withdrawal is not qualified, you will owe regular income tax plus a 10% penalty.  Using the money for a qualifying first time home purchase will exempt you from the 10% penalty but not the regular income tax.  To be "qualified," you must be over age 59-1/2 and the Roth account must have been open at least 5 years. 

From the IRS:

There is a set order in which contributions (including conversion contributions and rollover contributions from qualified retirement plans) and earnings are considered to be distributed from your Roth IRA. For these purposes, disregard the withdrawal of excess contributions and the earnings on them (discussed under What if You Contribute Too Much? in chapter 2 of Pub. 590-A). Order the distributions as follows.

Disregard rollover contributions from other Roth IRAs for this purpose.