I can speak to starting an animation in the middle. In the case of montage, just create a section for your position you want to start at, then call Montage_JumpToSection with the section’s name. For regular anim sequences played via animation blueprints, you can expose the Start Position via a pin on the sequence player node and pipe the time value you want into it.
One use case for State Machine Conduits is in providing common transition logic instead of duplicating that logic across multiple transitions, e.g. the transition to the conduit takes care of the ‘common’ (e.g. is moving) case and the transitions out of the conduit can be more specific (e.g. is crawling, is running, is walking).