The primary purposes of the questions are to determine: 1. if an amateur athlete can be a sole proprietor since sponsorship (in exchange for promotion of the sponsor) is income (note that he is not a professional athlete); 2. if this is a business, then is sports equipment (which are necessary expenses in order to run the business) expenses that can be claimed for tax purposes.
Note that this question comes from the athlete looking to: 1. avoid the option of having a trust account; 2. decrease taxable income via business expenses.
An answer other than "speak with an accountant" is what I'm looking for. The whole purpose of posting my question here was to avoid having to find and speak with an accountant.
It is possible for an amateur athlete to set themselves up as a sole proprietorship. However, you should talk to an accountant or someone else who knowledgeable in this area before making you decision. Some sports organizations may also have rules that insist that you set up a trust rather than a sole proprietorship, or other rules that may affect how you handle your sponsorship income.
This does not respond to all aspects of the question.