Questions & Answers about Sono felice che il topo non sia qui.
Why do we use sia here instead of è?
Because Sono felice expresses an emotion. In Italian, verbs showing emotion or personal attitude trigger the subjunctive mood in the following clause when they are connected by che. sia is the present subjunctive form of essere (to be) for he/she/it.
Could I use di + infinitive here, like Sono felice di non essere qui?
Not if you are talking about the mouse! You only use di + infinitive when the person doing both actions is the exact same (for example, 'I am happy that I am not here'). Because the subjects are different here—you are the one who is happy, but the mouse is the one who is not here—you must use che followed by a conjugated subjunctive verb.
Why is non placed after the subject il topo?
Could I use qua instead of qui at the end of this sentence?
Yes! qui and qua both mean 'here' and are virtually interchangeable in this context. qua can sometimes suggest a slightly broader general area, but either one works perfectly to say the mouse isn't around.