Is it true that for the method to be stable it always hold that:
For Euler's Method: $ h<\lambda/2$ EDIT: Is there a difference in this between the explicit and the implicit method?
For Runge-Kutta(4): $ h<\lambda/2.78$
With $h$ being the stepsize and $\lambda$ the eigenvalue.
Which eigenvalue should we take? The greatest or the lowest?
EDIT: Is there a similar formula for the trapezoidal method?
No. What you probably mean is $|λh|<2$ and $|λh|<2.78$ if $λ$ is the largest eigenvalue and all eigenvalues are real and negative. This has to do with the stability regions (z=x+iy=λh)
If you want some kind of stability for more general problems with complex eigenvalues, one would have to chose something like $ |λh|<0.5$ for Euler and $ |λh|<2.5$ for RK4.