I am getting requests to connect via remote desktop

[theedudenator]

I have had a few instances where someone is trying to connect to my remote desktop.

Is this someone trying to do this? Or something with the software?

Do I need a firewall? Or blocking some ports?

[patrice4419]

Perhaps a firewall will do - try ufw and also gufw. Most distros have them. Well Mint 16 does as I installed it.
Sudo ufw enable
Sudo ufw default deny
sudo ufw allow out 53,137,138/udp
sudo ufw allow out 20,21,22,25,80,139,443,5900,8001/tcp
sudo ufw deny out to any

This was picked up from one of the many instruction web pages ( there must be millions by now) but it works.
gufw is the graphic interface - you might not want that but it is easier to manage the firewall.
You can set other ports of course, just make another rule.