1) That depends a lot on where you want to go first, there are about 10 trains daily from Hungary to Romania using various routes.
The usual option is the EN473/Ister overnight train - it leaves from Budapest at 19.10, crosses southern Transylvania (stopping in many cities along the way, including popular tourist destinations like Sighisoara and Brasov) and arrives in Bucharest at 12.10 .
2) If you only want to visit a single place you won't really need a guide.
Take the IC407/Corona overnight train from Budapest to Brasov (17.40 > 8.53) then the bus to Curtea de Arges (9.50 > 14.28) and next a local minibus to Capataneni (nearest village to the fortress). Get to the fortress (a one hour walk along the Transfagarasan road + a climb to the top of the hill it's located on), visit it in the afternoon then return to Capataneni and spend the night at one of the many guesthouses there.
Next morning head back to Curtea de Arges, take a bus to Ramnicu Valcea then a train or bus to Sibiu. Try to visit some of Sibiu's medieval downtown, then in the evening make your way to Medias or Alba Iulia and catch the overnight train back to Budapest.