I agree with the consensus to find another shop. These issues you describe are not uncommon, but they're not universal, and should not be accepted as the norm. That said, I have a few suggestions for the future, since you may encounter other ops like this again.
The main thing that concerns me is that the guide refused to surface when you indicated you were low on air. Unfortunately, this seems to be fairly common, as I've heard a lot of stories like that here, but it is not OK. It puts you in a terrible position; it's not safe for you to stay with the group and risk running out of air, but it's also not very safe to surface alone. For future reference, the latter is better, and better still if you can shoot a DSMB and ascend together with a buddy.
I'm also a little concerned that in so few dives you received two faulty pieces of equipment from this shop. As others have said, these kinds of malfunctions do happen, they can be missed even by a careful shop, and it's ultimately your responsibility to check your own gear--but their equipment does not seem to be up to standards. Still, I would recommend getting your own computer, and practice disconnecting the inflator hose and orally inflating. You might want your own complete set of gear eventually, but a computer is relatively inexpensive, doesn't take up much space or require much maintenance, and since the layout of information varies so much, it's nice to have the same one every time.
The fact that they gave you less weight than you asked for is more annoying than concerning. As has been pointed out, many new divers are overweighted, but I find it odd that they would think 4kg was too much for someone in a 5mm, even with a steel tank. I've had the opposite problem, with a guide telling me I needed more weight and then, when I declined, sneaking it onto my rig. In the beginning, it's reasonable to be open to a shop's suggestions for amount of weight. But I would encourage you to do a proper weight check at the end of each dive, and once you know exactly what you need, insist on it. (A proper weight check involves hovering at 5 meters with 50 bar and being neutral with no air in your BCD. If you have more than 50 bar at the end of your safety stop, you can purge your octo to get rid of some air. A weight check at the surface with a full tank can help get you close to where you need to be, but doing it at the end of the dive is the best way to be sure for the next dive.)
The fact that buddies weren't assigned and buddy checks were skipped is further evidence that this operation is a bit too casual about safety, though if that were the only issue I'd hesitate to condemn them. If you don't have regular dive buddies, it's a good idea to chat people up on the boat as early as possible and try to find someone to dive with. Best case, you'll make a new friend. But when you have a decent guide, you're not really solo even if you don't have a buddy.
I think it's OK for a new diver to go a little past 60 feet. But if they took you there without warning, that's also not cool. My first two post-OW dives were with a very good private guide. He gave me a thorough briefing, gave me a chance to ask questions, and for the second dive asked me if I was comfortable going a little deeper, to 70 feet (21 meters). I was nervous, but he had earned my trust with the first dive, so I decided I felt comfortable pushing my limits with him. I would not have felt comfortable if he had surprised me by taking me to 70 feet without discussing it first.
The main thing that concerns me is that the guide refused to surface when you indicated you were low on air. Unfortunately, this seems to be fairly common, as I've heard a lot of stories like that here, but it is not OK. It puts you in a terrible position; it's not safe for you to stay with the group and risk running out of air, but it's also not very safe to surface alone. For future reference, the latter is better, and better still if you can shoot a DSMB and ascend together with a buddy.
I'm also a little concerned that in so few dives you received two faulty pieces of equipment from this shop. As others have said, these kinds of malfunctions do happen, they can be missed even by a careful shop, and it's ultimately your responsibility to check your own gear--but their equipment does not seem to be up to standards. Still, I would recommend getting your own computer, and practice disconnecting the inflator hose and orally inflating. You might want your own complete set of gear eventually, but a computer is relatively inexpensive, doesn't take up much space or require much maintenance, and since the layout of information varies so much, it's nice to have the same one every time.
The fact that they gave you less weight than you asked for is more annoying than concerning. As has been pointed out, many new divers are overweighted, but I find it odd that they would think 4kg was too much for someone in a 5mm, even with a steel tank. I've had the opposite problem, with a guide telling me I needed more weight and then, when I declined, sneaking it onto my rig. In the beginning, it's reasonable to be open to a shop's suggestions for amount of weight. But I would encourage you to do a proper weight check at the end of each dive, and once you know exactly what you need, insist on it. (A proper weight check involves hovering at 5 meters with 50 bar and being neutral with no air in your BCD. If you have more than 50 bar at the end of your safety stop, you can purge your octo to get rid of some air. A weight check at the surface with a full tank can help get you close to where you need to be, but doing it at the end of the dive is the best way to be sure for the next dive.)
The fact that buddies weren't assigned and buddy checks were skipped is further evidence that this operation is a bit too casual about safety, though if that were the only issue I'd hesitate to condemn them. If you don't have regular dive buddies, it's a good idea to chat people up on the boat as early as possible and try to find someone to dive with. Best case, you'll make a new friend. But when you have a decent guide, you're not really solo even if you don't have a buddy.
I think it's OK for a new diver to go a little past 60 feet. But if they took you there without warning, that's also not cool. My first two post-OW dives were with a very good private guide. He gave me a thorough briefing, gave me a chance to ask questions, and for the second dive asked me if I was comfortable going a little deeper, to 70 feet (21 meters). I was nervous, but he had earned my trust with the first dive, so I decided I felt comfortable pushing my limits with him. I would not have felt comfortable if he had surprised me by taking me to 70 feet without discussing it first.