1. In Finland, the municipalities design and manage the local bus routes. Most of these don't extend to neighboring municipalities, but in some cases, the agency that manages public transportation is a joint one between several municipalities. This is the case in the capital region, where Helsinki Regional Transport Authority (Finnish acronym HSL for "Helsingin seudun liikenne") includes seven member municipalities. HSL is currently in the process of moving to a zone-based pricing similar to e.g. Stockholm, but currently the ticket prices depend on whether the trip crosses the borders of a municipality. There is a "local", within-municipality ticket and a more expensive "regional" ticket (I guess similarly to the Russian system). For a bus from Helsinki to Espoo on a HSL bus you'd need the regional ticket, even though the trip may be a lot shorter than one within Helsinki.
Other larger cities, such as Turku, have just recently started a transport authority organization that includes the surrounding municipalities. At the same time, the Finnish state is about to start a major reform of the municipalities themselves, and in the lead-up to that, many municipalities have merged with their neighbors. In many places, the borders of the municipality will include a very large area. E.g. Oulu is on its way to include all of the municipalities that were its neighbors ten years ago.
Matkahuolto is a service company owned by a union of the long-distance bus operator companies. Matkahuolto manages the pricing, ticketing and parcel service on the long-distance buses, whereas the buses themselves are operated by different private companies. It's effectively a publicly sanctioned cartel, and up to this year, there has been effectively no ticket price competition between the operators. This year, a discount bus operator named Onnibus started traffic. Onnibus operates outside of the Matkahuolto cartel and in many cases is not allowed to use the bus stations in cities. Their pricing is similar to discount airlines in that seats are available at different prices, with a limited number of very cheap tickets available in a web store only. Tickets bought from the bus driver can cost substantially more.
2. The fares are set separately by each municipality (in some cases via the joint authority such as HSL). The price level depends on the amount of subsidy that the municipality has decided to spend on public transport, and the operation costs and the income from tickets, of course. There are various types of discounted tickets for frequent users, monthly or yearly transport passes etc. The discount is often quite substantial. Hardly anyone who uses HSL's services to commute to work every day pays the single ticket prices.
3. Long-distance bus tickets always include a seat, at least if bought before the trip. I don't think it's legal to carry standee passengers on long-distance buses (someone on the forum can correct me on this). In local traffic, the ticket price is the same for everyone, and whether you get a seat or not depends on the level of crowding. It's up to the driver how many people he or she allows on the bus. There are regulations about the maximum number, but of course, it's difficult for a driver to know exactly how many people there are.
4. Not sure. See
Onnibus is at http://www.onnibus.fi/, but their pages seems to be in Finnish only.
By the way, it's "suomen kieli" with an 'i' at the end. In Finnish, the name of the country is written with a capital letter ("Suomi"), but the name of the language is not ("suomen kieli" or "suomi").