So Vanya has externalised her issues to a huge extent - Hope has spoken to her a few times and is pretty much able to pick them all up: she's afraid of science; she wants to be useful and to have a purpose; she thinks she's unlikeable and she lacks self-awareness. This is why he is taking their threads very carefully; he is working on establishing boundaries for their relationship. For example, the ear piece! if he cannot talk to her for whatever reason, he's just going to say so. (This is in part Ronan's problem - he won't tell her that he can't cope right now whereas Hope would simply request that she come back later so that he can give her his full attention). If he's busy he will say so, but also give her a time when she can talk to him again. Basically, he's kind of very aware that Vanya could go from needing reassurance to being kind of a leech on him, emotionally, and he thinks the latter is a very bad idea. So he's setting up boundaries.

They're not friends as that would be kind of the definition of creepy. But they are some kind of guardian/charge relationship.

As for Hope's lab! It's locked to him, and if you go inside it doesn't look that flash. There's a really comfortable chair though, because Hope canonically never sleeps so he needs a comfortable chair to pass out on for a few hours.

But on a serious note there's a bunch of datapads lying around that light up because that's what Academia uses all the time man. The white board on the wall is covered with scientific equations and notes to himself that make no sense to anyone except him given that he and Alyssa invented time-space theory. There's always at least one moogle in his office, old coffee cups lying around and on the desk are a bunch of prototypes that he's working on. He has tools in the drawers and basically his office is kind of crazily cluttered.

One thing you want to do with each of your characters?