Does a disabled person that lives with me and to whom I am his Caregiver and since I paid for than half of the living expenses, qualify as a dependent

Yes, if the person lived with you year-round, then he may qualify to be your dependent under the Qualifying Relative Test. 

1. The person either (a) must be related to you or (b) must live with you all year as a member of your household. 
2. The person's gross income for the year must be less than $5,050 (social security does not count) in 2024
3. You must provide more than half of the person's total support for the year. 
4. The person must be a U.S. citizen or a U.S., Canada, or Mexico resident for some part of the year.
5. The person mustn't file a joint return with their spouse with the following exception -
   You can claim a person as a dependent who files a joint return if that person and that person’s spouse file the joint return only to claim a refund of income tax withheld or estimated tax paid.