I would recommend that you NOT book all these flights on one ticket. If you did, and then wanted to change your schedule while in Europe all the remaining flights would be repriced and you'll have to pay a lot more. Plus, if you missed any flight, the ticket would be canceled and you would lose ALL remaining flights, including the return to Vietnam.
And, in this case you don't need to put all the flights on one ticket. You only need (or should) to do that if your onward flight is immediately after an inbound. But you have several days between flights so the chances of missing the next flight due to a delay are minimal to zero.
Here's what I would do. Book your HAN-LGW and FRA-HAN flights on one ticket using open jaw. Then look at your European schedule and book appropriate, separate one way flights. Take TP's advice re the train between Venice and Rome.
You may also find low cost carriers with cheap one ways. EasyJet springs to mind, and they would not have showed up on your multi city search as they don't support interline ticketing with other airlines. But they would be a perfectly good point to point option and operate from LGW and Southend.