This tutorial will give you some good pointers for some general security measures to take with your server:

• 7 Security Measures to Protect your Servers

If you are allowing remote access to MongoDB, I’d also suggest implementing firewall rules that restrict what IP addresses are able to access it. The following would allow SSH access on port 22 and restrict incoming access to Mongo’s default port (27017) to a specific IP address:

sudo apt-get install ufw
sudo ufw default deny incoming
sudo ufw default allow outgoing
sudo ufw allow ssh
sudo ufw allow from ip.address.to.allow to any port 27017
sudo ufw enable

This tutorial from the MongoDB docs should point you in the right direction for learning how to backup a MongoDB instance using the mongodump tool:

• Back Up and Restore with MongoDB Tools