I have personally answered all of these questions many times in these forums and in detailed format. You need to get better at using search.
Anyway, I will give an overview but you can then search for specific threads.
1) Very generic and broad question as there are many complexities in the Saudi visa process. On an overall basis, the process is totally different to Bahrain. Your employer gets a visa quota issued or has existing visas for your nationality / profession dedicated to your home country.......provides a bunch of documentation (will vary based on different criteria), you add your medical results and attested degrees and apply in the KSA Embassy. When you get visa, you arrive here, get finger printed at the airport, undergo medical, get insurance and iqama is issued. The whole process from start to end can take months depending on many variables such as availability of visas, consulate requirements etc. Iqama itself on arrival can be done in a week or can take a month. So no hard or fast standards for Saudi
2) Yes. Degrees need to be attested first by Saudi cultural mission and then by the KSA Embassy (birth / marriage certificates only by the KSA Embassy). Forget Bahrain and don't compare it to Saudi - they are different countries. Saudi is really particular on attested degrees and painfully matches your degree to the profession on your Iqama to the job that you are going to do (Any mismatch and you will face trouble e.g. you can't have an IT degree and then say you are working in Finance........have experience of 20 years in Finance, tough luck, you can't work in Finance without a Finance degree). Also be ready for the fact that as an engineer, you will need to go through Saudi council registration & verification process (after arrival) which in itself is cumbersome (Bachelor of Engineering degree and at minimum, 4 years of certified professional experience). So make sure that the profession on your work visa (and then Iqama) has the word Engineer in it or you will get such a painful landing which you can't imagine. On the second part, KSA Embassy in Bahrain will not attest documents that are not issued in Bahrain and will refer you to the issuing location's Embassy. This means that if your degrees are from India then you need to approach Saudi culture/Saudi Embassy there for attestation.
3) This I have answered in a lot of detail. Your visa can ONLY be done from Bahrain if you have a valid residence visa, your current company gives an NOC to the KSA Embassy and most importantly, your employer has an existing quota to dedicate a visa to the Manama consulate (see point 1 - this is not possible for most employers in 90% of the cases. Again, I have explained why in the past). Just some examples:
https://www.expat.com/forum/viewtopic.php?id=1021215
https://www.expat.com/forum/viewtopic.php?id=988388
https://www.expat.com/forum/viewtopic.php?id=832371
4) NOC and Good conduct certificate from Bahrain are only needed if you are applying for KSA visa from here
5) Yes you can go via the causeway. Fingerprinting and photos will be done there. Family can go on visit visas (as family visas need your Iqama to be in place). They will then need to leave KSA to get family visas stamped from whichever consulate of KSA they are eligible to apply in
6) You need to have a "family status" contract from your employer, have a job profession on Iqama that allows you sponsor family members (i.e. can't be labor or low level professions) and have a recognized bachelor or better degree which corresponds to your profession (the last one is something immigration have decided to bother people on in the past few years e.g. many people with ACCAs or similar qualifications were being told that this is not a degree). And yes, there is a medical for family members in home country and on arrival as well
7) The one advice, if you use search, that I always give people is "NEVER RESIGN UNTIL YOU HAVE THE VISA IN YOUR HAND". And that applies double for Saudi
8) There are many depending on your budget. High end ones like Allied pickfords will cost you a pretty penny
9) Yes it is possible to import. Full process on car import / export to and from KSA has been listed on the Bahrain and Saudi Arabia forums by many members. And if you are moving to Saudi for good i.e. will lose your Bahrain residence then it is better to export car as you won't be able to do registration renewal etc., without a valid CPR in Bahrain. Some examples:
https://www.expat.com/forum/viewtopic.php?id=658066
https://www.expat.com/forum/viewtopic.php?id=1021835
10) Yes license can be converted. Again, the whole process is listed on the Saudi Arabia forums
Saudi is not an easy landing for anyone. The visa / on-boarding process is the most bureaucratic and complex that I have faced in any GCC country. Don't even consider Saudi unless you are someone who has a lot of patience and can go with the flow of things.