The speed limits in Lithuania are 50 km/h (50 mph) in built up areas, 90 km/h (56 mph) outside built up areas, and 130 km/h (86 mph) on motorways
In Lithuania the motorways and the non motorwary main roads are both called A roads and the smaller roads just have numbers.
I never rode on the motorways in Lithuania so I cannot comment on them. The main roads that I rode on are of a poorer standard than those in the rest of Europe that I have ridden on to date.
The A road motorways signs have a Green background with Red/White numbers, the non motorway A road signs have a Blue background with Red/White numbers, and signs for the smaller roads have a Blue background with Yellow/Black numbers.
In was only in Lithuania for 2 days, to go from Poland to Vilnius and then to return by the same route, therefore I have limited experience of the roads in this country.
Petrol at the time of writing it was about 1.30 Euros per litre.
I never saw any signs for speed cameras and I never saw any patrolling police vehicles.
I did not buy a SIM card for a mobile phone whilst I was in Lithuania so I have no information about how to do this.