hi there,
Frequent trains run between Rome Termini and Milano Centrale train stations. A few fast trains also leave from Roma Tiburtina station.
The fast Eurostar Altovelocita (ESA) trains make the trip from Rome to Milan in as little as 3 1/2 hours although some take 4 hours. Eurostar (ES) and Intercity (IC) trains take from 5 to 6 1/2 hours. The fastest ESA trains cost almost double what the IC
trains cost. You'll need to reserve a seat but you don't need to change trains to get between Rome and Milan. Trains leave from early morning until about 11:00PM.
Rome-
Athens
I think the cheapest way is to take a train from
Roma Termini to Ancona (about 3 hours) and from Ancona take a ferry to Greece.
In the summer there should be 2 or 3 ferries a day traveling to Greece, this might be the cheapest but time consuming as it will take you about 20 hours from Ancona to Greece.
Athens-Cairo and Cairo-Germany
I think the easiest way and cheapest will be by plane on these last destinations, check with
Cyprus Airways, and Egypt Air for flights from Cairo to Germany
Happy travels