Depending on your mother's income, you may be able to make a claim for 'Infirm Dependant.' Your mother does not own her home so she is not able to claim the OSHPTG, however yes she can make a claim for the OEPTC. Without knowing where your mother lives, we can't say if she qualifies for the NOEC, however if you review this link you can see if your mother qualifies.
http://www.fin.gov.on.ca/en/credit/noec/
