I think he means something like: "At least I will wear a charm for you so that you don't need to suffer after this." (Or does he mean that she will wear it? I'm a little confused because of "君に" in the second half.)
It is the listener, and not the speaker, who will be wearing a charm.
「君に～～をつける」 means "(I will) attach ~~ to you".
I don't really understand what he is trying to say in the middle part (embedded question?) because the verb is passive and he is the doer.
He is not the doer. He is saying that he might not be permitted. The person who might or might not permit is the listener and not the speaker.
So is he saying something like: "I don't know/understand if this situation (こんなこと? the fact that he didn't save her parents?) will be forgiven by myself, but..."?
Sorry to keep replying negatively, but the answer is 'no' again. (You may be reading something that is way above your current Japanese proficiency.)
Judging from the context that you have given, the speaker is talking about whether he would be permitted to attach that charm to her without her consent. He is worried he might not be permitted to do so by her. Thus, 「こんなこと」 refers to the speaker attaching the charm to her.
(If, however, the larger and unprovided context suggests that 「こんなこと」 would refer to the fact that he didn't save her parents, you would need to show it to us. Normally, that would be much too serious a matter to describe as 「俺に許されるのか分からない」. What happened already happened. Why would he wonder if he would be allowed to let it happen after it happened?)
And does から at the end refer to the previous sentence about the charm? That he (or she?) will wear a charm because he is worried about her?
Yes, it does. It is like saying 「それでも心配だから,
I did it. (= attached the charm to you)」.
It is very common to end a sentence with 「から」、「だから」、「ので」, etc. unlike in English.