Philosophy struggles to find the right tone of voice to address questions which, like yours, arise out of suffering as well as curiosity. But here goes. It’s sad to see someone with Alzheimer’s partly because it is they who are diminished by it: the pity is that there’s a continuous personal history which includes both your aunt as she once was and the disintegrating person you now go to visit. So I’d say it’s still her.
On love: it matters hugely to small babies to be touched, held and so on – as we say, loved – and they cannot manage the thought that the person holding them today is the same as the one who did so yesterday. So I’d say the same for your aunt. And thought aside, who’s to say that your aunt doesn’t know your touch so being touched by you makes her feel loved in a way she wouldn’t if touched by a stranger?