Can I apply for my mom on Visitor visa (I am green card holder)

Assuming that you mother has no bars to enter into the United States and is from a Country that is not visa waiver or exempt, she can apply for a visa to enter as a visitor to the United States. She will need to show that she has times to her home country intent to return and that she will be supported while she is here. An invitation letter from you explaining that you will help take care of her needs while she is here is something that can be helpful.

No. Visitor's visa requires no application by the third party. You mother needs to apply on her own.

If you are asking whether you and as a Green Card holder can petition for your mother, or a any parent for that matter, the answer is no, only a US Citizen can do this. A Green Card holder can only petition for his or her spouse and/or child or unmarried son or daughter. Speak to a qualified immigration attorney

If I understand correctly, you are inquiring whether you can apply for your mother while she is in the U.S. on a visitor visa? If so, the answer is yes but this may not be the best option as her visitor visa is a nonimmigrant visa which requires that she not have the intent to immigrate to the U.S. You should consider consulting an attorney via Skype or in person for a more thorough analysis of your specific situation and for a discussion on the options available to you.

Whether your mother qualifies to come on a visitor visa will depend on the exact circumstances of the visit. If she intends to come for an extended period of time a different visa may be a better fit for her. You should schedule a consultation with an immigrant attorney to get advice tailored to your situation.