Today I received a dismissal letter with three...

If you are an expatriate in Kuwait and work under a work visa with a scientific qualification later here, note that according to the Labor Law that the employer can terminate the work in accordance with legal rules and he can force you to leave if you are on their sponsorship, they may also give you the no-objection to transfer the bail where the text of your work law
the termination without legal reason is arbitrary dismissal and the employer has to pay compensation and end of services benefits if the worker worked for more than a year, if you worked for less than a year then you will get only compensation.
For the termination during the probation period, according to the law, the employer is entitled to ask for compensation. If you applied for resignation and applied the notice period that mentioned in the law, then you can leave the work and get benefits at least after 10 days.
For termination and cancellation, below article states:
Article (44)
In the event where the term of the work contract is not specified, both parties shall have the right to terminate the same by means of a notice to the other party as follows:
a- Three months prior to the termination of the contract for the workers earning a monthly remuneration.
b- One month prior to the termination of the contract for other workers.
In the event where the party wishing to terminate the contract does not abide by the period of notice, he shall be obliged to pay the other party a compensation for the notification period equal to the remuneration of the worker for the same period.
c- In the event where the notification of termination is issued by the employer, the worker shall have the right to be absent one day or 8 hours per week in order to search for other work. He shall also be entitled to his remuneration for the day or hours of absence.
The worker shall decide on the day or hours of absence and shall notify the employer at least one day prior to such absence.
d- The employer may exempt the employee from work during the period of notification while but shall count such period within the worker’s period of service. The employer shall pay the worker all his entitlements and remuneration for the period of notification.

In all cases, the matter requires obtaining a non-objection from the first sponsor, in addition to that it is required that you have spent one year in the service of the sponsor, unless a waiver of this right has been written for the purpose of transferring the guarantee, otherwise he can file against you with an absconding report that results in the prohibition and your duty to leave the country