One-month notice is all it takes to quit the job

"Article 117 (1) - Both the employer and the worker may terminate a contract of employment of unlimited duration for a valid reason at any time following its conclusion by giving the other party notice in writing at least 30 days before the termination."
However, should you be working under a limited period contract, you may terminate the contract without a prior notice period but you may have to compensate your employer for an amount up to 45 days of your salary. This is in accordance with the provisions of Article 116 of the Labour Law that states:
"Article 116 - Where a contract is revoked by the worker for reasons other than those specified in article 121, he shall be required to compensate the employer for any prejudice the latter sustains as a result: provided that the amount of compensation shall not exceed half the worker's remuneration for three months or the residual period of the contract, whichever is shorter unless the contract contains a provision to the contrary."
Although your employment contract requires you to give a notice of three months prior to the intended date of termination, you may still leave your present employment on a 30-day notice. The provisions of the Labour Law mandate that in the event of conflict between concurrent provisions in the employment contract and the Labour Law, the provisions, which are more beneficial to the employee, shall always be applicable.
In view of the foregoing and in pursuance of the second part of your question, it may be advised that if the stipulated notice period prior to termination of an employment contract gets reduced (by either the employer or the employee), then the party responsible for reducing the notice period must compensate the other party for the reduced number of days. This is in accordance with Article 119 of the Labour Law that states:
"Article 119 - Where an employer or a worker fails to give the party notice of the termination of the contract or reduces the period of notice, the party obliged to give notice shall pay the other party compensation, called 'compensation in lieu of notice', even where no prejudice has been sustained by the other party as a result of such failure or reduction. The said compensation shall be equal to the worker's remuneration in respect of the entire period of notice or the time by which it was reduced. Compensation in lieu of notice shall be calculated on the basis of the remuneration last received, in the case of the worker remunerated on a monthly, weekly, daily or hourly basis or in the case of worker remunerated at piece rates, on the basis of the average daily remuneration referred to in article 57 of this law."
However, if you fulfil the requirement to serve a minimum notice period of 30 days, you are not obligated to compensate your employer for two months' salary. Hence your employer may not be within its rights to deduct your two months' salary.

How to avoid a labour ban
I have been working with a Ras Al Khaimah-based company on a limited period contract since April 2014. My designation according to the employment visa is 'computer operator'. When I was interviewed for the job, my employer had said my salary would be increased from Dh1,250 to Dh1,500 once I start gaining experience. I also have an e-mail he sent in which this point has been mentioned. It has been one year now and I have not received any increment. Is there any way for me to change my job before completing two years?
I have a bachelor's degree in commerce. When I called the Ministry of Labour call centre, I was informed that job change is possible only if I get offered a salary of Dh7,000 or above from a new employer. But this is not possible. If I get an offer letter of Dh5,000, then based on my matriculation certificate, can I avoid a ban? Is there any other way to avoid a labour ban?
Pursuant to your question, it may be noted that an employee who may terminate his employment contract before completion of two years, may have to face an employment ban which may be for a period of six months to one year, during which period the employee may not take up any other employment in the UAE. The ban may be lifted if a prospective employer offers a salary corresponding to the educational qualifications of the individual, which in your case is a minimum of Dh7,000.
Additionally, it may also be noted that after the completion of two years of continuous service, an employee may not have to face an employment ban if both the employer and the employee have agreed to such termination of the employment contract. This is in accordance with Article 2 of the Ministerial Order No. 1186 of 2010 on "Rules and Conditions of Granting a New Work Permit to an Employee after Termination of the Work Relationship in Order to Move from One Establishment to Another" (the "Ministerial Order"), which states:
"Article (2) - The following two conditions must be met in order to grant the work permit mentioned in Article (1) of this resolution:
1. Agreement between the employee and the employer to conclude the work relationship.
2. The employee must have spent at least two years with the employer."
Pursuant to the foregoing, if you can secure a no-objection letter from your current employer, no employment ban should be imposed on you.
Further, it is learnt that employment ban issued by the Ministry of Labour may not be applicable for entities established and based in free-zones of UAE. And therefore, you may also explore the possibility to seek employment in such free-zone entities even if an employment ban is imposed on you.
Pursuant to the last part of your question, you may check with the Ministry of Labour if you can have an employment ban lifted based on your matriculation certificate and an offer letter from a prospective employer, offering you a monthly salary of Dh5,000.