I want to warn you that any donation that benefits a specific person may not be deducted as charitable contribution. Please see for reference the IRS publication 526 - http://www.irs.gov/pub/irs-pdf/p526.pdf If you would take a donation from people - you should not mislead and provide the correct information this matter.
The answer on the first question depends how you earn the money. If the money coming as gifts - the gift is not taxable income for the recipient. However if the amount is above $12,000 (for 2008) per person per year - the donor would be required to file a gift tax return (there will not be any gift taxes unless the lifetime limit of $1,000,000 is reached) - if the donor pay directly to medical facility for the treatment - such a gift is not taxable despite its amount.
If the money would come as income from some business activity - selling goods, providing service, etc - you may want to set-up a non-profit organization and ask for exempt status - so such profit will not be taxable. You will also need exempt status if you purchase any goods (for instance a pizza for fund raisers) and want to save some money on the sales tax.
If you plan to solicit donation s from general public - please be aware that the Tennessee Charitable Solicitations Act requires that charitable organizations who solicit contributions directly or indirectly from, or within, the State of Tennessee register, unless exempt from the registration requirements. Organizations that are exempt from the registration requirements of the Act include bona fide religious institutions; educational institutions and supporting organizations composed of parents of students and other persons connected with the institution, which are organized and operated for the purpose of conducting activities in support of the operations or extracurricular activities of such institutions; volunteer fire departments, rescue squads and local civil defense organizations; political parties, candidates, and Political Action Committees; hospitals; and organizations that receive annual contributions less than $30,000 from the public. Groups that are exempted purely because they receive annual contributions less than $30,000 are required to complete and file an "Exemption Request" form with the division. - http://www.state.tn.us/sos/charity/chforms.htm
The Tennessee law provides "Catastrophic Illness Trust" as the option for your situation - it is defined as a trust or custodial account established to benefit those with a catastrophic illness, or a severe illness requiring prolonged hospitalization and/or doctors and medicines. Trustees or a bank or trust company acting as trustee are required to provide notice to the Division of Charitable Solicitations on establishment of the trust. This notice is required before soliciting donations in the State of Tennessee. - http://www.state.tn.us/sos/charity/catastrophicAct.pdf
The trustees, other than a bank or trust company acting as trustee, are also required to file with the Division of Charitable Solicitations an annual accounting of the trust on the anniversary of the establishment of the trust. This accounting must include all revenue and expenditures of the trust. The trustees must keep true and accurate financial records of the trust for no less than three (3) years. In addition, the Secretary of State may compel additional production of documents, exhibits, or things by any person which the Secretary believes to be pertinent in conducting any investigation.