1. To jog one's memory is to do or say something that causes the person to remember something (I think the common Russian way of saying it is всколыхнуть память). Thus, 'jogger' here is 'one who jogs', in the sense of it's one who stirs something up (memories in this case). The last three words are actually a compound noun, if it helps you can think of it as 'jogger-of-memories', it's three words used to express one concept.

2. I can see how it might be confusing, as it might appear that 'hopeful' describes how the sister feels. As a native English speaker, I understand 'hopeful' here as implying that the protagonist is visiting his sister hoping that something she will say or do will help him remember whatever it is he's forgotten (jog his memory), but he isn't really sure whether it'll work, just hopeful that it will. That is, 'hopeful' here modifies the idea of her being a 'jogger-of-memories', it doesn't describe how the sister actually feels about the situation (if that's what was confusing to you).