Let me take a stab at the first question: You can give away (either during your life or upon your death) a certain amount of property without incurring gift or estate taxes. The amount used to be about $600,000.00 but I think it's more now.
Each year, however, you can give away up to $10K per person that does not count towards the $600,000.00 (or whatever it is now). If, however, you give away more than $10K to someone during a year, I think you have to file a gift tax return. You can choose to apply the amount of the gift exceeding $10K towards the lifetime $600,000.00 or you can choose to pay gift taxes currently on that amount.
The above applies to the gift giver only. The lucky recipient does not have to pay taxes on any gift, no matter what size.
If this is wrong, someone please jump in and correct me!
I have no clue about the tax consequences of annunity proceeds. One place to start would be to call the annuity company and see if they can answer the question themselves. You might also want to check the IRS web page to see if they have any pamphlets that address the issue.
Good luck,
Ed