So my question is, can they claim any money from me?
The Basic Conditions Of Employment Act:

Deductions and other acts concerning remuneration
34. (1) An employer may not make any deduction from an employee’s remuneration
unless—
(a) subject to subsection (2), the employee in writing agrees to the deduction in
respect of a debt specified in the agreement; or
(b) the deduction is required or permitted in terms of a law, collective agreement,
court order or arbitration award.
(2) A deduction in terms of subsection (1)(a) may be made to reimburse an employer
for loss or damage only if—
(a) the loss or damage occurred in the course of employment and was due to the
fault of the employee;
(b) the employer has followed a fair procedure and has given the employee a
reasonable opportunity to show why the deductions should not be made;
(c) the total amount of the debt does not exceed the actual amount of the loss or
damage; and
(d) the total deductions from the employee’s remuneration in terms of this
subsection do not exceed one-quarter of the employee’s remuneration in
money.
(3)A deduction in terms of subsection (1)(a) in respect of any goods purchased by the
employee must specify the nature and quantity of the goods.
(4) An employer who deducts an amount from an employee’s remuneration in terms
of subsection (1) for payment to another person must pay the amount to the person in
accordance with the time period and other requirements specified in the agreement, law,
court order or arbitration award.
(5) An employer may not require or permit an employee to—
(a) repay any remuneration except for overpayments previously made by the
employer resulting from an error in calculating the employee’s remuneration;
or
(b) acknowledge receipt of an amount greater than the remuneration actually
received.

Regarding your notice period:
Notice of termination of employment
37. (1) Subject to section 38, a contract of employment terminable at the instance of
a party to the contract may be terminated only on notice of not less than—
(a) one week, if the employee has been employed for four weeks or less;
(b) two weeks, if the employee has been employed for more than four weeks but
not more than one year;
(c) four weeks, if the employee—
(i) has been employed for one year or more; or
(ii) is a farm worker or domestic worker who has been employed for more
than four weeks.
(2) A collective agreement may permit a notice period shorter than that required by
subsection (1).
(3) No agreement may require or permit an employee to give a period of notice longer
than that required of the employer.
(4) (a) Notice of termination of a contract of employment must be given in writing,
except when it is given by an illiterate employee.
(b) If an employee who receives notice of termination is not able to understand it, the
notice must be explained orally by, or on behalf of, the employer to the employee in an
official language the employee reasonably understands.
(5) Notice of termination of a contract of employment given by an employer must—
(a) not be given during any period of leave to which the employee is entitled in
terms of Chapter Three; and
(b) not run concurrently with any period of leave to which the employee is
entitled in terms of Chapter Three, except sick leave.
(6) Nothing in this section affects the right—
(a) of a dismissed employee to dispute the lawfulness or fairness of the dismissal
in terms of Chapter VIII of the Labour Relations Act, 1995, or any other law;
and
(b) of an employer or an employee to terminate a contract of employment without
notice for any cause recognised by law.

So they could probably apply any leave due to you against the 1 week short notice.

I'm with Basement Dweller, just go and get on with your life.