Yes, all of the voice/text/video/screen packets of discord are relayed through their own servers and the connection is not P2P (Peer to Peer).
You can block the display of the following: link previews, images directly uploaded, image link previews.
No, their are virtually no security problems with Discord as far as I know, you are able to set weather you'd like to scan all received DMs or not, who can add you as a friend and if you'd like to be able to receive DMs from fellow members in a server that you're in.
Personally, I love Discord and will never go back to Skype.