Hitchhiking works very well (check Hitchwiki), you might be asked for money, though if you make sure before to enter saying: "bezplatna" (in Russian) or "fara bani" (in Romanian) for free, you'll avoid any problem for sure. Local transportation is also very cheap (city buses for around 0.1/2€) and mid distances buses also shouldn't be very expensive.
Not so many hosts on hospitality exchange networks, though good street hosting and people spontaneous hospitality.
Street food is very cheap (be careful with the quality) as also supermarkets. Dumpster diving can be very challenging for your health, street markets are better than supermarkets for this.
wifi quite hard to find especially outside of cities (still very possibile in restaurants etc) and internet cafés often available.
Russians and former soviet countries passport holders don't need any visa and can stay with no limit(?). EU citizen get a free stamp on arrival which should last 3 months.