The insurance may or may not be taxable to your mother. If taxable she should receive a 1099-R that shows the taxable amount. Whether taxable or not depends on many factors that only the payer of the policy can tell you. What she does with the money has no brearing on the tax whatsoever. Gifts are never taxable to the receiver of the gift, but the giver might need to file a form 709 for a gift more then $15,000 to any one person.
Maybe. There can sometimes be a tax due on gifts. This tax is the responsibility of the person making the gift.
Gift tax returns (Form 709) are due (but not necessarily a tax) for gifts that exceed the annual exclusion for each year. If your mother has re-married she and her spouse may elect to split gifts and effectively double the amount she is allowed to give to you and your brother each under this exclusion.
The annual exclusion amount is currently $15,000 per person. This means that your mother (and her spouse, if applicable) can give you and your brother each $15,000 per year without a tax consequence. If she gives you just $15,000 per year each, no return is required. If she and her spouse elect to "split" a gift and give you each $30,000 a return is required.
While exceeding the annual exclusion requires that a return be filed, a tax won't necessarily be due because there is another exclusion that comes into play called the lifetime exclusion.
The lifetime exclusion amount is a little different because it applies to the total amount your mother can give away to all people and that amount is currently $11.58 million. (This amount, if she elects to split gifts with her spouse is $23.16 million.)
No tax is due until she exceeds this amount in gifts that she gives all people, in cash and non-cash items over the course of her entire lifetime.
This includes all gifts except:
The above covers federal gift tax. If you live in Connecticut, you also have a state gift tax to contend with and should consult a local adviser for more information about that.
TurboTax does not support the gift tax form and if you are looking at a significant transfer we do recommend that you and your mother find a qualified professional in your area to discuss this matter with before you transfer any funds to ensure that you do so in the way that will be most beneficial.
Also, a good adviser can assist you with the best ways to deal with the funds once they are in your possession.
Here are a few resources that may be helpful for you:
If your mother gives you more than $15,000 in one year she will have to file a gift tax return, Form 709, as macuser_22 said. She will not actually have to pay any gift tax unless all the gifts she has given in her lifetime are more than $11.5 million, but she will have to file the gift tax return. If your mother's total assets are anywhere near $5 million she should consult a tax professional before making any large gifts.
Your mother might need professional help to file the gift tax return. TurboTax cannot be used to file a gift tax return.