is it true that for every Solomonoff-like priors, shorter program have almost always higher probability than longer ones? Almost always in this case means "all but a finite number".

No, that's not true. You can take any infinite set of pairs of programs and swap the weights in each pair.

I guess that one can prove this is not the case for computable priors.

Yeah, all universal priors are uncomputable. For any computable prior, you can build a computable sequence whose probability under that prior is 0. For example, you can ask the prior "which choice of next bit would have probability below 0.6?" at each step.