I've thought of a few different answers to all three of your questions but frankly the scope of your questions would require me to write a dissertation.

Europe, even as a continent is a pretty huge place and within the span of 100 years attitudes towards artists/artisans would change over this time. Your question about arts education is also difficult because education within 100 years over an entire continent changes and varies also. I will however try and answer your questions based on my understanding of the arts during this time in Northern-ish Europe (UK, Low Countries, Germany, France)

During this time most artists/artisans (artisans is probably a better term to use) were sons (occasionally daughters) of traders, merchants and craftsmen. Becoming an artisan followed the same route as becoming any other kind of crafts-person, which was joining a studio/workshop as an apprentice and depending on skill would end up helping to paint backgrounds and auxiliary figures in commissions received by the artist who ran the workshop, their master. If their skill and experience grew they would eventually leave their master and open a workshop of their own, taking their own apprentices and the cycle would continue. It's worth noting that most workshops undertook many different kinds of work including goldsmithing, sculpting, painting and architecture to name a few. Most apprentices wouldn't go on to open their own workshop and would instead become journeymen, either staying at the same workshop or moving to others.

The use of the title 'artist' as someone who painted/drew/sculpted is a more modern invention and at the time it was common to use the catch-all term 'artisan/crafts-man' when referring to a person who made things/objects as their profession.

The social position of a master was a relatively influential one and on the same standing as a merchant or anyone else who owned a business and had people working for them. Under the masters socially were the people who worked for them, apprentices, journeymen etc who were considered skilled workers. Under skilled workers came unskilled workers and so on. In today's terms master's could be considered middle-class, skilled workers lower-middle-class and unskilled workers were working-class.

As to whether a parent would want their child to become an artisan depends on the social standing of the parent in question. Parents who owned a workshop would want their children to continue in their own line of profession and take on their business. If they already had a son/s as their apprentice then they probably wouldn't dislike their child joining a different workshop as an apprentice and would want them to be successful. Children from parents of a lower social standing would want their children to gain a higher social standing by apprenticing and becoming a master/business owner themselves, so wouldn't be disappointed (I imagine).

Parents of the upper classes/nobility wouldn't look favourably on their children joining an artisan profession as working for a living was something the 'lower' classes had to do and since most noble families drew income from land rented out to tenets, wasn't something they needed to do.

Education is a tricky one. About a third of the population of this time were educated. It's safe to assume that the level of education depended on whether that person was going to inherit/run a business (which means reading, writing and maths were needed). Education in a trade (painting, goldworking etc) was undertaken as an apprentice in the workshop and not something one learnt at 'school'.

For the upper-classes education usually happened at a university. They would go off to university at around age 14 and learn the 'seven liberal arts' which were arithmetic, geometry, astronomy, music theory, grammar, logic, and rhetoric. After they had completed 6 years of study and gained their 'Master of Arts' degree they could either continue to study law, medicine or theology or go home and do something else. So basically, painting, drawing and such things weren't taught at establishments in the way they are now and usually someone would develop an existing talent in their own time but there weren't art schools.

I hope I have answered your questions enough to help you undertake your own research/study in this vein. I'm no expert and I've tried to only give an outline of what is was to be an artist/artisan at this time in Northern Europe. The life of an artisan could be very different depending on what country you were in and the level of your skill.