Contract terminated during probation - exit / iqama question

Dear all - I have been in the kingdom for a few weeks.  Unfortunately my employment situation has not worked out and I have been terminated during my probation.

I already have an iqama which theoretically allows me to stay in Saudi for a year. 

The economy is hot here and I would prefer to stay and look for another job (of course I understand my iqama would need to be transferred to the new employer.)

however my current employer (I’m serving garden leave) wants to issue me with an exit visa and send me home. 

question one - does my employer have to issue me with an exit visa in which case I have to leave in a few weeks or can my company allow me to reside in Saudi for the rest of the iqama active time while I seek a new role?

(To be clear my company has already told he they will be issuing me an exit visa which means I believe I will need to leave in October 23.) 

Question two - assuming the company issue Ke the exit visa and by some miracle I find another job quickly in saudi - can my company still transfer my iqama and cancel the exit visa? 

(The Saudi visa process took ages!  I’d hate to do it again.)

apologies I’m sure it’s a stupid question.  I’m very new and would love some guidance.