Hi and welcome to Just Answer!1.
As a recipient of the gift (or inheritance) - the person does not need to claim it as income. Regardless of the value. Please see for reference IRS publication 525 page 31 (left column) -http://www.irs.gov/pub/irs-pdf/p525.pdf
4.All expenses paid for another person regardless of relations would be considered as a gift - for gift tax purposes. Exemptions are only for those specifically exempted.Please see IRS publication 950 for reference - http://www.irs.gov/pub/irs-pdf/p950.pdfpage 3 left columnThe general rule is that any gift is a taxable gift. However, there are many exceptions to this rule.
Generally, the following gifts are not taxable gifts:
•Gifts, excluding gifts of future interests, that are not more than the annual exclusion for the calendar year,
•Tuition or medical expenses paid directly to an educational or medical institution for someone else,
•Gifts to your spouse,
•Gifts to a political organization for its use, and
•Gifts to charities.
5.The grandparent may pay any expenses for the child including auto expenses - that is not an issue.However as long as such expenses are above annual threshold which is for 2013 $14,000 - the amount above would be considered a taxable gift. Still - none will be taxable for the recipient. The gift tax return is required when the total value of the gift is above $14,000 (for 2013) per person per year.There will not be any gift taxes unless the lifetime limit of $5,250,000 (adjusted every year for inflation) is reached.
Is tutoring handled the same as Tuition?
Yes - if paid to a qualified educational institution.
See the law section - http://www.law.cornell.edu/uscode/text/26/2503
(e) Exclusion for certain transfers for educational expenses or medical expenses(1) In generalAny qualified transfer shall not be treated as a transfer of property by gift for purposes of this chapter.
(2) Qualified transferFor purposes of this subsection, the term “qualified transfer” means any amount paid on behalf of an individual—
(A) as tuition to an educational organization described in section 170 (b)(1)(A)(ii) for the education or training of such individual, or
(B) to any person who provides medical care (as defined in section 213 (d)) with respect to such individual as payment for such medical care.
see section 170 (b)(1)(A)(ii) here - http://www.law.cornell.edu/uscode/text/26/170
(ii) an educational organization which normally maintains a regular faculty and curriculum and normally has a regularly enrolled body of pupils or students in attendance at the place where its educational activities are regularly carried on,...