All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is confirmed that the Prophet saw a man walking between graves while wearing leather shoes, and he ordered him to take them off. [Abu Daawood and others]
However, the majority of the scholars are of the view that it is permissible to walk in the graveyard while wearing shoes, and they interpreted the narration to mean that he ordered the man to do so, because such shoes were only worn by rich people, so, he disliked him doing so while inside the graveyard.
Nonetheless, some scholars are of the view that it is disliked to walk in the graveyard while wearing shoes. Different scholars have different opinions on this issue, however, in Islamweb we adopt the opinion that it is permissible to walk in the graveyard while wearing shoes.
With regards your second question, please refer to Fatwa 82461.
Allaah Knows best.