I don't find her attachment too odd tbh. She tells the Mc to abandon his old worlds common sense so she has been here for a long time. I forgot the type of isekai she came by did she start as a baby? She is probably happy to have a guy to interact normally with after all that time.
the stuff he bought was using shards. The otherworlders get shards every month based on viewer count. You can convert 30 shards into 1 point. He obviously didn't have enough shards for using the 2 or 3 he did at that time to matter.
I'm not sure of it was introduced by this point of the story of the webnovel but some of the otherworlders are employing this tactic. Apparently the god's camera is liberal with sexual content so there is someone going around brothels copying Interspecies Reviewers as well as someone NTR 'ing...
If I remember correctly the gem allows him to check on them and get a feel of their location. They can't do the opposite and are unaware of this feature. I remember a bunch of comments how stalkerish the gem was when he gave it to them as well. So yeah there is no way for them to know he is...
I think its just one of his spare coats that probably has the same design. Sora probably isn't carrying around clothes that would fit a child so just put that on her since it's probably the only thing that would fit without falling off.