Is this arrangement protected by copyright?
There is no doubt that the original Bach composition is public domain - that is, it is not protected by copyright. Whether a modern arrangement is a copy and therefore not protected or a derivative work therefore protected depends on how substantial the change is from the original.
This arrangement is probably different enough from Bach's simply because it will be written in modern musical notation - a language unavailable to Bach. It may also be an arrangement for instruments that didn't exist for Bach: like the piano. It will, therefore, probably have a copyright of its own.
Unless it's a copy of an intermediate arrangement that is itself under copyright but let's not go there.
So, probably, it has copyright, and for you to use it, you have to do so with permission - the licence is that permission.
This licence allows you to share and adapt the work, providing you give attribution.
Am I allowed to perform this arrangement in public?
Yes, that's an adaptation.
Would I be required to give attribution to the person who arranged the sheet music before performing the arrangement?
You must give attribution. Before, at the same time immediately after are all good:
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
You could do this by making an announcement, including the information in a programme, on a website about the performance, or any other reasonable way of getting the message out there.
Moreover, am I allowed to record the music in the arrangement and post it online (say on YouTube)?
Yes, that is an adaptation (film) of the adaptation (musical performance) of the original (sheet music).
What kind of attribution would I be required to give in this case?
See above.