What was the status of merchants during the feudal age in Europe? Did they, like peasants, serve/have allegiance to certain land owning lord? If yes, do they have different status or privileges from usual peasants? Or are they free from allegiance? If the latter, how did they become free from feudal lords who were generally powerful?
Merchants during the feudal system, tended to be Jews or other "foreigners." Lombards, Genovese and Venetians, (from the most entrepreneurial parts of Italy), and Greeks, tended to perform this function in northern Europe, Dutch (and other western Europeans) in Eastern Europe, etc.
Merchants were basically independent of the feudal system, being neither landowners nor peasants. As such, they were regarded with suspicion by the local elites. Their main selling point was that they had good connections with foreigners who could help them procure scarce goods. Hence, they were likely to be "foreign" (rather than local) members of a given society; most locals would not want to take on such a "foreign" role, at least at home.
Merchants weren't particularly well respected, but they were tolerated, and were allowed to live a bit outside the usual rules because they performed an essential (trading) service.
First of all, peasants were not slaves or anything like that. They were essentially renting a given lend, and most often than not they came into this relationship volunteerly as free men. In many if not most lands and eras getting free from this relationship was actually possible, and peasants could move to another landlord. After bigger wars or diseases that killed large part of the population of a given area, settlers from other lands are often came to work on the empty land.
While the relationship of feudal landlords and peasant were not rosy, being landless (therefore independent from a landlord) was not difficult - being landless AND SURVIVE in an agriculture based society, that was difficult. For certain ethnics and religious were even forbidden by law to work as a peasant, e.g. Gypsies and Jews in Eastern Europe.
Back to your original question: There were all kind of different kind of merchants. Some could have special status, or altogether could form independent communities. Merchants generally formed guilds to control and regulate local trade and negotiate with authorities. As cities are natural market centers and trade-posts, these guilds could give much power to a city or town. Many cities had local independence or were independent states. Independent state means independent not only local feudal rulers, but independent from kings, having own legislation, army, etc. Such city states with elected civil leaders were actually very common along major trading routes (e.g. Venice and Italian city states), and these cities often formed alliances (The Hansa or the Strasbourg-Zurich-Bern-Basel alliance) to protect themselves.