Need a 2nd hand car for 3 to 6 months. What should I choose?

[tetelee]

If you buy lunch, I'd be happy to assist you in the art of buying used.

How nice of you. I'll PM you when I have time

[mdn]

When I resell it, I am hoping that I will lose 1K at most.

Do you have a Finnish name? It does matter when you will try to sell it as a private person. As you might lose more than 1K even in case of try of immediately sell (after purchase) for a cheap car in nice condition, just due to your name (and a lot of time).
Anyway, even 500 euro car can be 'sold' to dealer for 3000 euro, as a 'take in' for a newer car (current offers Huindai and Kia).
When you are buying a car from dealer, you are paying 2K-3K more (in case of price range 4-10K, comparing to nettiauto private sellers), usually you are paying them just for a washing and half a hour car check.

He said I may sell it for 3.9K after 6 months but only as private seller (they may take it for 2K). When I asked the guarantee, he said they don't provide guarantee for such an old car.

Try to ask about those 2K after 6 months in a written form. 99.9% they will not get it back at all, even for 1K - without exchanging it to another their car.

Another guy from another dealer (I can't remember the name) wouldn't give me an ESTIMATION on how much they would buy the car back when I sell it 6 months later

It really hard to say for them as it depends to the amount of discount they are ready to do for a car you will buy at that time. For example, for 7K car - they are agree to take in your old car for 1K, for 12K car - already 2K for the same old car, and so on.

The cars I saw were all recently (within one month) finished inspection

A real case from my life - a car successfully passed inspection and the clutch has died when I tried to drive home from Katsastus.

So if a car passed the inspection last month, does it mean I should expect it to run for a couple of months IN GENERAL? And is an extra pre-sell check necessary for dealer-sold car, which was inspected last month?

Check an info about the particular car model, for example from TÜV auto reports and so on.

3) of course I am aware that if I sell it to a dealer they pay less)?

No, it depends to the price, and dealers' cars are usually much more expensive, so they are selling also not very fast.

4) Is there any suggestions on my situation?

Try to find someone who is a specialist in cars, and ask him to evaluate the used car state etc.