Medical schools that select for interview purely on UCAT scores will send out invitations quite soon. We receive results from UCAT at the end of this month, so don't expect anything before then. Some of those schools will have all of their interviews done by Christmas. Anywhere that has to read personal statements or other written submissions will obviously take longer: some of these will be interviewing in December but will still be sending out interview invitations in February.
Once interviews have happened, some applicants will get offers or rejections quite quickly; others will have to wait. Some places don't make any offers until all the interviews have taken place, while others will operate floating thresholds, where they can offer to high-scorers and reject low-scorers but have to wait longer to make decisions on those in the middle. In theory you should have all decisions by the end of March, but at least one medical school was still interviewing after this last year.
Quite a lot of interview candidates arrive with parents or partners, often because they're too nervous to travel by themselves, but there will be a point beyond which accompanying people aren't allowed. Sometimes candidates will go to a waiting room where they sit with the other candidates away from everyone else.
It can get really boring for accompanying parents. Your son/daughter will probably want to arrive super-early and there will then be a lot of waiting around. There might also be more than one thing they are supposed to attend (interview plus medical school tour with current students, for example, or an additional numeracy and/or literacy test). I've seen parents flat-out asleep having driven sons/daughters a couple of hundred miles and then waiting around for several hours.
If the medical school is on the actual university campus, or in a city centre, I'd recommend going somewhere for coffee/lunch rather than waiting around in the medical school.