Processing time of work permit and TRP (Bratislava)

Hi all,

dobrý deň, I am Robin from India, I have been offered a long term onsite opportunity for Slovakia (Bratislava). I am expected to travel in a few months from now (Nov Protected content . I was checking the processing time for work permit and TRP, I found both to be of 90 days each, so the total time is Protected content . If any of you have travellers recently from India. Please help me with the time lines.
I am so concerned because my wife is carrying and her due date is in march Protected content from now. I wish all the processing should complete only aftet her delivery, because the visa my company can provide is a single entry visa.

Also will i be able to add my baby as a dependant later. I believe visa is not needed for babies right.

Sorry for posting many questions in one thread. Thanks for looking into this.

Robin