The best advice I can give you along with what you've already had is what I was taught as a youngster and have lived by to this day - find a strong routine and stick to it as rigidly as you can - I don't just mean 'go to the yard every day at 4pm' (although it's nice if sharers are consistent in that way) but more that you have an itemised list/method of how you work with your horse/pony that never changes - so mine goes something like, arrive on yard, put my bag down, put on riding hat and gloves, fetch headcollar/leadrope from store room, go to stable, greet horse, put on headcollar, lead horse out, tie up on yard, fetch skipping out equipment, skip out stable... and so on and so on. It sounds silly to write it out like that and of course I don't have to consciously think about it anymore as it's so ingrained but the benefit of doing things in the same order and same way always are (a) if you have a fixed list of jobs you are less likely to forget to do things whether big and important like picking out his feet to make sure there's no stones before a ride or small but annoying if you don't do like putting kit back where you found it (b) this is the way to keep yourself and people around you safe, a lot of safety things like always checking your tack over and making sure everything is done up and not flapping before you get on have to get drilled in as habits because 99.9% of the time they are 'pointless' ie your girth isn't worn away and about to snap, a loose horse isn't about to charge at you through that field gate you carelessly left ajar to turn around to pick something up or whatever - but you'll regret not doing it the one time you didn't check/close the door/tighten your girth, so you need to get yourself to the point where you're doing these things mechanically almost. (c) if you always interact with your horse in similar ways, e.g. on first coming into their stable you approach quietly, speak to them softly and give them a little pat before immediately putting headcollar on, this will be both reassuring to the horse and also give you a chance to notice quickly if there's something unusual in their demeanour. I know as soon as I walk into his stable if there's something 'off' with my boy as he's nearly always in the same corner chomping hay and will always prick his ears and look up at me as I come in so if he's huddled at the back not interacting or pins his ears back at me, something is off (on the other hand some horses are always grumpy when you first come into their space, that's normal for them, you just have to get to know them as individuals), whereas if half the time I'm plugged into my phone or chatting to someone else or if I sometimes rustle food at him and sometimes creep up on him silently, how he reacts would naturally be different each time and I wouldn't notice as quickly how he is that day.... Routine is boring but everything with horses!
The other thing I'd say is if anything seems not right even if you can't explain exactly what, if he just 'feels' wrong or looks wrong or you aren't comfortable for any reason, stop what you are doing, get him and you to somewhere safe e.g. lead home if out hacking or back into his stable, and seek help. Ideally from his owner or the yard manager or member of staff, but if not then any experienced horse person so one of the other owners will usually be happy to help. Again even after 50 years riding and owning horses there's still things that flummox or worry me, sometimes they turn out to be nothing at all and I feel a bit of a naa-naa for asking but far more often I'm glad I did. It would be great to do some reading on the various ailments and injuries horses can have so you can spot early if something 's up but actually the advice usually boils down to 'call the vet' anyway and that would be for the owner to do not you, as would things like changes to his rugging, clipping, feeding, tack arrangements anyway so really your judgement call is only ever whether this is something his owner needs to know about, and in the early days I'd always err on the side of 'yes' even if it seems trivial (my boy is on long-term loan to me and in the first week I had him I called up his owner a bit worried because he wouldn't stop itching his forehead, I was worried he'd developed sweet itch or mites or something but she laughed at me and said he was just itching because, well, he wants to itch, he's an itchy horse, always has been always will be, but I'm still glad I checked!