Family Visit visa (1 Month) ----Yes
Family Visit Visa extension after a Month (Need Medical Check up in MedCom)- Yes, but it will not show FIT online
Residence Visa (Under your sponsorship)- Yes they will send her to rumaillah (CD) for Cleansing,TB culture, etc for free
Residence Visa (employment) - Big No.... there is no documents can support her as it will always show scar on the lungs every time she will undergo X-Ray
I hope this help mate......cheers....