87/88 626 2.0Diesel temperature problem?

I just bought a second hand Mazda 626. After some driving around I noticed my fan wasn't working and found a screwed fuse. Replaced the fuse and fan is working.

But!

The fan starts straight away. Even if the temp is completely low. Is this normal? Shouldn't there be a thermostat or something? How can I check that?

And the temp-needle on the dashboard goes up till half. And when it's half or just a bit more, the RPM of my engine in neutral is 2000 instead of 1000! Anybody who knows where I should start looking??

Or is it this serious that I have to go to mechanic straight away?

Thanks!!!