Hello Marten,

Firstly, please note that the sample size is very small (in a path model you need at least 10 observations per relationship, not to mention that at least a hundred ob observations is desirable) -- even though you would be able to estimate the coefficient, it might be biased because of small sample. The fit statistics may be inadequate because of that as well, since RMSEA, for instance, is dependent on the sample size.

Secondly, note that the standard errors are rather larger in comparison to the estimated coefficients -- this also indicates that the model is misspecified.

Thirdly, from the RMSEA that you mentioned, only the second one falls within an appropriate range. Please refer to this presentation for additional information --

http://www.psych.umass.edu/uploads/people/79/Fit_Indices.pdf
Key question -- is there a way to increase sample size?

Additionally, please consider least squares estimator and 2 stage models in particular -- this would allow you to model your relationships and check the robustness of the SEM estimates (even with low sample size).

As for saturated models, honestly, I have not looked into those for a long time and cannot say anything about them.