Cost of commuting daily between Bahrain to Khobar (Saudi)

1) 25 SAR each way.  Total 50 SAR for return trip
2) Go check on bahrain.bh for King Fahd causeway insurance - shows for Bahrain number plates cars going into Saudi and for non-Bahrain cars entering Bahrain, both.  Yearly should be around 60 BD or so.  You can get it online or at the causeway - for Saudi cars, as you exit, the insurance booths are right there.  For Bahrain cars, you have to get it from the insurance booth BEFORE passing causeway toll on the right as you approach the causeway
3) See this thread:
https://www.expat.com/forum/viewtopic.php?id=765888
4) Not without NOC from the Bank
5) No. But you might need to have Saudi driving license if you are a resident in Saudi