This is basic stuff who is build-in feature, IP > DHCP Server..
At LAN network you can assign a IP who will be working as gateway for your LAN devices. When they use your IP as gateway then it’s done for routing. They can use DNS from any remote services like 1.1.1.1 etc.
You must do a IP Firewall Nat a new rule with masquarade action, typical SNAT chain.
You say you use a QuickSet, then you should have this done too.
example
About Telit, you can found some tips here http://forum.mikrotik.com/t/telit-lm940-how-to-get-working/127619/1