As caregiver to disabled vet for 9 years (recognized and compensated for 2 years), how and for what do I claim (gas? Food? Rent? Etc?)?

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Do you live with this person?  What are you in relationship to this person?  Are you getting a W-2?  If you are getting a W-2 nothing is deductible on your federal return as employee job related expenses are not deductible.  Some states do however allow expenses. 

If this person is a spouse, family member or companion, you cannot deduct gas food or rent. 

Rent would not be a deductible business expense even if you are self-employed.  The only time rent would be deductible as a business expense would be if you have a home in one location and have a temporary home in an area due to needing to stay in that area temporarily for business. Temporarily would mean less than 12 months tops. Food is not deductible for yourself when you are just working throughout the day.  

Gas, if  you are getting a 1009-NEC would be deductible as a mileage business expense for times you are transporting this person.  

So, what you can deduct, if anything will depend on how you are paid, what your expenses are for and who you are taking care of as well as which state you live in.