Supports taking kills happen...there's been games when I've had more kills as a Support then my ADC. Never happened on purpose and definitely felt bad about taking them, but it happens, either miscalculated my damage, their adc walked into CC, or it was either kill them or be killed. I'm not going to sit there and give them a kill if i can kill them first if my ADC isn't going to react in time, or I don't think my ADC will react in time.
I've flashed in as Janna to get an auto off to finish off kills before because my ADC wouldn't do it. At the end of the day, we got the kill.
Yes she was wrong to not stop last hitting if you asked her politely. A lot of people see the PROS last hit for the Pro ADCs and assume that's what they should be doing as well...monkey see, monkey do. Honestly when I was forced to play support role (before I started learning the role) I'd do the same....you just try to copy the pro players because you want to be like them. But there's no sense arguing with someone you'll chances are never see again, or won't see for 100+ games or more. Much better just to mute and ignore and focus on then the mini game of "lets see if I can last hit before my jerk support does"
As I said previously, why she didn't initiate with the ult I don't know....maybe she used it as a means so they don't escape? I couldn't tell you...yes if I was in her shoes, I'd use it early to mid fight to disrupt not as an execution. So her doing that at the end was the wrong play, I completely agree with you there.
People are in bronze for many reasons....some just have awful mechanics, some just are casual, some play the blame game, some don't think they have anything to improve, and some are flamers/ragers. Though there's always exceptions, the higher up in elo you go the less blaming of others you will see, the less raging (plat elo is exclusion...that elo is toxic as F i've heard).
I have a friend stuck in Bronze. He's been there for 3 seasons. He's an ADC main and I'd say a pretty good one too mechanically wise. But heaven forbid if his support or jungle messes up. It's the immediate blame game, flames them, and he just auto tilts. I'm in no way stating this is what you do...I'm just giving an example here. But because of this blame and flaming, he upsets the whole team, and even if he is correct and the jungler or support is an idiot, it puts the team on edge and effects gameplay and costs him games. His blaming and flaming is what keeps him in bronze, even though mechanically he plays ADC probably as well as a silver.
ANY....ANY....ANY support that starts Dorans is putting themselves behind and doesn't know what they are doing. They will be behind in gold....they lost the lane right there IMO. As for Morgana, she's probably still hands down one of the top 5 best Mage supports IMHO. I'm not talking about her damage. I'm talking about her utility. Her snare which lasts forever. Her shield which stops ALL CC (say bye to thresh hooks....blitz grabs...Taric stuns). If I was an ADC main and I had to choose one support (who was knowledgeable mind you in the support) I'd want a Morgana by my side every day.
If they are going all AP, they aren't playing to give up kills...they are building to be that extra damage person late game. Yes they should still play support role in laning phase and still be somewhat supporty later too.
Just keep in mind though, you are bronze.....as you said, most people either are casual or just are bad. That's why I greatly suggested learning to 1v2 and not rely on a support. Find that ADC that you can 1v2 decently with if a situation comes. For me, mine was Jinx. If I felt that the connection between me and my support was missing, I'd pick Jinx because I knew I could at least farm and somewhat peel if I needed for myself (or them if I needed to).