Coming to Ba

1) You can get a phone number at the airport.  Most providers have their offices in the arrivals hall.  They are also offering internet packages through mobile devices or fixed
2) Unfortunately, public transportation here is nothing like the UAE.  They only started bus services a year ago which is cheap but I am not sure about the coverage / routes.  You can google.  Alternative options are taxis or careem/uber
3) Overall job market in the GCC right now is very very bad.  Due to lower oil prices, there is somewhat of an economic recession with layoffs and downsizing everywhere.  In addition, the governments are cutting subsidies/levying VAT so everything is increasing in price.   

In addition, Bahrain is a very small market compared to UAE / Saudi with most of the white collar jobs in the financial services industry.  On top, the Bahrain locals are more educated / qualified vs. their Saudi counterparts so expect more competition as an expat.  I don't know your profession or job target so can't be more specific here.