Most of time my prints fail due to lack of support and "base" for the 3D model. I'd like to know if there is any software that can automatically check my model, and add support and a "base" to it, if required.
This program type you seek for is called a slicer. However, you got to manually choose support structure and rafting - the tricky part is getting the configuration right for your build. To my knowledge there are no slicers that decide automatically to raft unless you configure to raft always and you have to enable support.