These are both very good questions; and they have essentially the same answer.
Everything depends on the verbs, as usual.
- until you listen/start listening to me
- I hope/I'm hoping that
Listen is a sense verb. It describes a volitional human activity that can be continued indefinitely.
Predicates referring to acts or states with duration can refer to the beginning of the duration, the ending, or the time in between. Start specifically refers to the beginning, which in this case refers to a single volitional action on the part of the addressee (you). And if you start listening to me, then you listen, at least a bit, and that means the same as you listen to me. So there's no difference in meaning, in either case. Rather, the two constructions get to the same place by different routes.
Hope is an emotional verb, a human emotional state that can be continued indefinitely.
The Progressive construction (a form of be followed by the -ing form of the next verb in the chain)
is normally not used with stative predicates, since they are already continuous, and the purpose of the Progressive is to add continuity to a static event description. Thus,
- He is renting a house in Ypsilanti. (grammatical, since rent is active)
- *He is owning a house in Ypsilanti. (ungrammatical, since own is stative)
But emotions, while continuous, can change in degree, and emotional predicates used in the Progressive therefore refer to the constancy of the emotion.
In both I'm hoping and I hope, I'm in a hoping state, so there's that same effect again.
Basically, I'm hoping means 'I still hope'.