I would like to make two points.
1 You are allowed to offset a truly amazing amount of expenditure needed when moving house / job
against tax. Keep every bus ticket, train ticket etc. whatever and everything relating to your previous residence
and setting up a new.
(extra costs of running two homes can be offset up to a period (I forget how long)).
2 The normal method here is that the first six months are "Probezeit" - testing period.
This is followed by a formal interview and you will soon get the feeling as to whether you are useful
to the firm or not.
If you get the thumbs up then ask for more dosh to bring you up to the market rate.
Remember than unless you have fluent German you are at a disadvantage and often less valuable
to your employer than a native speaker.
That being said, there is supposedly a shortage of Engineers in Germany - but only in certain
restricted areas. You are expected "to hit the ground running".
As a "Green" I'm no enthusiast for cars, but I can hardly see how you can set up house in rural Germany without one.
Furnished accom. is not the norm here. But why worry -
Ikea, Roller, Domäne, Hüfner etc. have endless
furnishings at all price levels. If you don't want to do the work yourself, there are ways and means!