All the economy of this small country is based on middle-high class tourism. Although is a very safe country it is also very closed minded and quite conservative (due to historical reasons and influence of the near bishop). The main "city" is all about posh shopping but the country have some amazing views and great hikes to make, specially in summer.
No railway inside the country, but there is a well developed bus system. Hitchhiking is also possible, specially during winter. Might be harder in the main valley, but easier on the smaller roads. The bus are quite expensive 1,85 euros ( March 2017 prices) per ticket regardless the number of stops and without transfer ( you take another line, you pay another ticket). The buses usually pass every 15-20 min. Last bus is usuallyaround 20:30-21 h
Andorra is an expensive country to stay in regarding accommodation, but there are some tricks. Spread across the country there are mountain refuges that you can use for free. Mostly there's no electricity, but there is a fireplace and running water from a well or source. For a complete list, see here. The shelters are technically open all year long but most of them are far, up in the mountain and the temperatures during the winter can be very low so be very careful. Is a very safe country so sleeping on the streets ( basically summer) should not be dangerous, however the police probably won't allow it. A small couchsurfing comunnity appeared recently.
In general, basic food is rather expensive ( slightly more than Spain, as a reference). Alcohol is cheaper.
All across the villages and cities you'll find free wifi.
Not recomended. Andorran authorities don't like street performers nor beggars because they aim for a "rich country" aesthetics. There used to be a law that allow to kick out of the country street performers and beggars, information about the validity of this law could not be found. However is not very backpacker/nomad friendly.