As with all questions about Europe in the middle ages, the answer depends on the time and place; however, speaking in general, the answer tends to be "no", but it depends on the profession. There's a series of books by Frances and Joseph Gies that I'll draw on for this answer; in particular Life in a Medieval Village and Life in a Medieval City, but all their books are wonderful reads if you're even casually interested in how people lived in medieval Europe.

In contrast with the popular imagination of the period, medieval society cannot easily be stratified into a neat hierarchy — the most popular vision of this is the pyramid, with the nobility on top, townsfolk beneath, and last/certainly least the peasantry at the bottom. Peasants could and would experience higher qualities of life than their town-dwelling cousins, depending largely on their ownership of land (or rights to work/lease it): at minimum, a family might subsist on a bit less than half a virgate (approx. 14 acres) of leased land, but nearly every village had families owning upwards of four times that amount, and those who owned or leased a hundred acres or more (with subtenants of their own, of course) would live lives just as (if not more) lavish than many nearby true gentry. And yet, legally these peasants, rich and comfortable as they may be, could still be bound to their status as villein: maybe bound to provide labor, perhaps unable to marry without permission, certainly obligated to pay taxes and fines, often as a way of waiving other obligations. Indeed, in some regions (particularly Germany) there were even those in the nobility who did not own their own freedom, known as the ministerales; these were legally nobles (usually knights), but essentially owned by another, and were thus unable to marry, pass property to their heirs, move, etc. without the permission of their lord.
To bring this digression back on topic, the point I'm trying to drive in here is that legal obligations and unfree status were not exclusive to peasants, to the economically downtrodden, or to any one class or rank in the medieval world.

So to speak to your question itself, tradesmen could be bound to the land, not because of their particular profession but for the same reasons a serf or peasant might be: because their parents were. In certain professions, this was more-or-less standard: the best example is that of a miller, as each village would have at least one (generally working a mill owned by the lord of the village, leased or "farmed" out to the miller's family for some kind of rent) who would grind the grains of the village's inhabitants for a fee. In this case, they might owe service just as would their neighbors, and they would certainly be obligated to the local lord's court and its rulings (never including death, which was almost always reserved to either the local nobility or the King/Emperor himself). Yet I claimed earlier that most tradesmen did not have such duties or obligations; given that we know that a man's wealth would not set him free, what would?

Towns and cities had special status: usually some form of autonomy, wherein the people of the town ('burghers') might elect a mayor or a council from among the city's wealthier inhabitants, which would then in turn be afforded some degree of self-governance. Most trades were not so conducive to operating in the countryside: the largest markets for goods were in towns and cities, and so that is where most tradesmen would tend to live, if not attached as a retainer to a lord (as was common with blacksmiths, for example). As such, a King who wanted economic prosperity would in many cases be inclined to help those cities and towns within his domain grow and expand, such that he could tax (and indeed buy) the new goods and services that the tradesfolk within could provide. A member of the landed gentry, however, would generally be unwilling to let too many of their unfree tenants slip the collar for a better life in the nearby town — and indeed, it was his/her legal right to fine those who did so and to plead his case in the courts if the peasant did not return. To manage these competing desires — that of the town to grow and expand, and that of the gentry to enforce their legal rights — most locales developed a legal principle along the lines of the German Stadtluft macht frei: urban air makes you free. In its most common iteration, if you could lie low within a city or town for a year and a day — hiding from the agents of your landlord all the while — you would be declared free, no longer a villein of the village but a burgher of the town.

Of course, there were other ways a peasant might make their way to the city; a free tenant could do so whenever he wished, but they were generally fewer in number, and a wealthier villein could purchase his freedom, but by that stage in life many didn't want to; the right of urban air, on the other hand, would allow a young man, perhaps one who anticipated little or no inheritance, to move into town and become an apprentice with a local guild, such that by the time he reached his mid-late 20s he would be a full member of the community and a productive member of the urban professional class.

Second question: The first question assumed that tradesmen usually held no land and only their homes. Is that assumption true?