"She is now working in Doha as office staff",,  ILLEGAL, because expatriates under Domestic (Qadama) visa is not allowed to work in any company.
 

2: The rule is since long time, that you can change your sponsership only after 2 year for the first time. but, Domestic visa is not transfereable to company visa, but, you can transfer Domestic visa only if the sponser is same.

3: Domestic (Qadama) visas are only for House work, like Baby sitter Etc.

4: Yes she can file a Case against her current sponser, but becarefull she will not get anything by doing this, & will be cancle soon from here. 

Though the company is giving the agreed salary (including the free transpo and housing allowance? She is still bother because she never signed any contract from them as of now

5: Company it self is voilating the law. Since 9 months they did'nt signed any contract and hiring staff for a specified on Qadama Visa.