Hi NightCabbage, you would generally make adjustments like you're talking about in a similar construction type way.

For example to "move that surface forward", you could select it, then run Construct / Extrude to build a new solid coming out from it, then select that new solid and the original one and do a boolean union to combine them together.

That kind of an approach of constructing an additional piece and booleaning it with your model would be the most regular way to do that kind of an adjustment in MoI.

But it is also possible to break things into individual surfaces and do a lot more "low level" kind of tweaks at the surface level. If you want some more information on doing that kind of a thing, check out this object repair tutorial here:
http://moi3d.com/forum/index.php?webtag=MOI&msg=446.17

But it does tend to be better to build your object more closely to what you want earlier on, rather than just make something sloppy and tweak it later like you might do in a polygon modeler.

If you want to do the "tweak a bunch later" kind of workflow, probably a polygon modeler is going to be a better fit with that style of modeling rather than MoI.

- Michael