Calculation of the lowest energy conformation with a webbased solution or freeware I like to draw a molecule in different conformations in a) website or b) freeware and 


Calculate its relative energy difference (for example to the lowest global energy conformation)
Display the lowest energy conformation


I'm particularly interested in the calculation of diaxial interactions, gauche interactions, double gauche pentane interactions (and less in ring strain, like chair / half-chair / twisted rings).

I know there are plenty of tools for modelling conformational and electrostacic properties. Most of those are not freely available. Do you an easy solution? 
It does not must to be the most precise one, relative energy differences in steps of 0.1 kcal/mol between two drawn conformations would be fine for me.

May be this question is off-topic, because it's a software request, but I didn't know where else I could ask this question.
Avogadro can do a lot of this for you. It might not be precisely what you want but the molecular mechanics from Open Babel integrated into it can do at least some of the tasks you mentioned. It's free and has a very intuitive and smooth user interface. A real pleasure. The downside is that it's poorly documented.

To play around with conformations, go to Extensions -> Molecular Mechanics. To view the generated conformers (from the Conformer Search option) go to View -> Properties -> Conformer Properties...