The gift letter is all that is necessary. You will need to write a letter of explanation yourself assuming the the gift is over $100. It is not required though highly recommended you keep the money in your main checking account as opposed to creating a separate savings account.
Any money you have in any of your accounts belongs to you and can be used to pay for both MRF and buy down. If you plan to buy down keep in mind your MRF doesn’t include buy down so your MRF will effectively increase by your buy down amount. Case in point you have an MRF of $5000 and you want to buy down $5000. You will need $10000 in your bank account.
Your buy down funds also must be in your bank account before you go to credit access. So if you expect to receive a gift then make sure you receive it no later then when you make an offer. Otherwise you will be under contract and your file will be paused without the ability to go to underwriting until you can show the deposit.
The gifts cannot be used for payment payment shock or to inflate your income.