Can I still deduct child care expenses (daycare and afterschool program), when my husband works full time and I am part time student and part time self-employed?

And can I still deduct tuition and business expences?

Those two items are unrelated to the dependent care credit.
You can deduct the business expenses, of the self employment, directly on Schedule C. You do not have to itemize deductions.
Tuition you paid may qualify for a tuition credit or, if related to your occupation, may be deducted on schedule C

Thank you!

Only if the self employment shows a profit (positive net income, after expenses).