I looked up the GSM coverage map from KPN - the former state telephone company - and virtually all of the IJsselmeer is covered according to that on 4G.
Can't tell from experience though but I'd gather you'd be in range on nights anyway. The IJsselmeer is large but not huge.
Before refrigeration salt was the primary means of preserving fish. As you mention in your question filleting them is a a good first step, they should also be dried to reduce the amount of salt needed.
But what you really want
Keep them alive, until you get home to clean, and freeze or refrigerate them. There are several solutions listed in When to ...
There is a website which has a map listing all public fountains, some examples of how the fountains look can be found here. But most Dutch people tend to be friendly, so if you ask them if you can "borrow" a few liters of water, they tend to laugh and be very helpful.
First of all, in the Netherlands camping in the wild is prohibited, and they really don't like it.
Now you're in need for some water, first the good news, tapwater in the netherlands is filtered and ready to drink but like you said, you won't find much public water because of the expenses that are needed to get the water to a fountain (you have no ...
I've wild-camped a few times in NL without problems. I guess it all depends on how well you hide and where you are.
Can't really help for rural area's. But in less rural areas:
Laundry: I'd expect laundry facilities for a few euro's in the poorer neighborhood of cities. Where students or immigrants live.
Water/shower: some truck stops/gasoline stations ...
What you are probably looking for is a satellite two way messenger like an inReach or to rent a satellite phone. The two way messenger will allow you to send both text messages and coordinates, and the inReach at least can be set to send up a message with your position every so often, and then your family will be able to track your route online.
You don't ...
To answer the title question, there are a number of diseases you can get from wild rabbits,
Zoonotic diseases specifically associated with rabbits include pasteurellosis, ringworm, mycobacteriosis, cryptosporidiosis and external parasites.
Rabbits can transmit bacteria through bites and scratches. One of the common agents involved is Pasteurella multocida, ...
About water, I cannot say that much. As long as the water is flowing, mostly it is good, however if there are agriculture lands around the river (which is very often the case), it might be filled with pesticides or other chemicals making you sick.
Except for bars etc, I'm sure most people want to give some water as water from the taps is really cheap. So ...