I can advise you based on my readings of Qatar Labor law and my 35 years of experience in Qatar.

A1. During your probation period, you are not entitled to any type of vacations except Sick leaves.
- If the company gave you approval to take day of, then it will not be paid.

A2. Depend on your Contract if it's (Local hire or overseas) if it is local hire and the employee decided to cancel the contract before one year, then the employee is not entitled for air ticket nor end of service benefits, unless your sponsorship is on the company and the company wants to cancel your contract/deport you.
However if your contract is overseas and the employee decided to cancel the contract before one year, then the company should pay you the air ticket keeping into consideration that your RP will be canceled.

Note: At all times you must provide a notice period for your employer/company for maximum of 30 days, subject to the request of employer according to the Qatar labor law.

A3. Employer/Company must provide air ticket back to your home every 12/24 calendar months, The air ticket should include your family aswell if you are married and you are the main sponsor of the family.

If you are not on the sponsorship of the company, then you have very weak powers to claim such rights, however it is all possible depends on your employer/company

There are many good companies in Qatar that will provide you with all these rights without asking for it, however you have to know your employer very well, check their reputation before you work for them, as after transferring your sponsorship your options are very limited.