Is it allowed for men to wear a wedding band?. Also is it wrong for them to wear a necklace (pendant) that bears the inscription of Bismillāh al-Rahmān al-Rahīm)

It is not disallowed for men to wear a wedding band unless of course there is some superstition attached with wearing it. Also, there is no harm in wearing the type of pendant you have referred to, if it is not made of expensive material such as gold etc.