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Hi and welcome to the Forum.

First off, that's a good salary; many people live on much less.  You've done most of the work already; my only comment is that they tend to reflect what happened historically; the nice apartments/houses that you see are almost certainly already gone, it is unusual for such houses to stay on the market for more than a month unless they need work doing to them or are next door to somewhere unpleasant.  To try and answer your specific questions:

1.  With renting anywhere in the Netherlands, opportunity very much drives house prices; if you want to live in the west in the big cities (and I would count Rotterdam in that), you will pay a premium.  Rental housing is always in short supply; the 30% of income rule is a general reflection of what people can afford and still live a relatively good life; it's not a hard requirement, some people have the attitude that this is probably their only chance, so are going to spend a bit extra.  My advice would be to plan to use something like an AirBnb for the first 3 months, then use that time to actually go and see, speak to people, get the advice of locals.  I would advise you to do as much checking on AirBnb as possible - look at references, check out the address on Google street view, I've seen reports of housing being put up for rent that just didn't exist or were not available.

2.  It's not a steadfast rule, they are your savings to do with as you wish, for example you will need to pay a deposit, most people use savings for that type of thing.

3.  You say you've used Pararius etc - the prices are there, they reflect current prices.  If something is cheap, there will be a reason for it, you need to check what that is.

4.  The landlord is looking to rent out his property as soon as possible for the rent he is looking for; nobody is going to set aside their property and wait for you to arrive 6 months down the line; if someone is, he/she are almost certainly scammers.  If something is too good to be true, it almost certainly is a scam; we've heard bizarre stories of people moving into their new apartment, to find someone else already living there.  Time, I would plan on using the first few days to sort out registration, bank account, doctors, etc, then go into house searching, some people take 3 months to find something they can live with.  Ask around at your new employers, who knows what may be happening?

5.  Groceries.  If you shop at the big supermarkets (Albert Heijn etc), you will pay more.  We tend to shop at the local market for all our meat, vegetable, bread, eggs, cheese and fish, then use Aldi, Jumbo, Lidl, the bottom end of the market place for the rest.

I hope this helps.

Cynic
Expat Team

Looking for a house or apartment with 3 bedrooms will be very hard in the region of Rotterdam within 5 months is nearly impossible. Especially if you are looking from a large distance.

It isn't impossible but the time to find a good place is very short.