Making beer happens to be part of my day job!
The basic steps are:
Growing Barley. CrHe opportunities, and possible weather magic options too.
Harvesting barley. Lots of ReHe opportunities here, transporting the harvested barley can be achieved by magic too.
Malting: this essentially involves drying out the harvested barley, and storing it for a month or so, then steeping it in water and putting it in a big damp pile until it just begins to germinate, and then drying it out again. After it's dried you can also roast it (which gets you dark malts). You can use magic to manage vermin and pestilence here and to dry/roast the malt. Also, note that you can do this with many other grains, not just barley.
Crushing the malt. Not to a flour, but the husk has to be cracked. Maybe a PeHe or ReHe job. Or some sort of animated (coarse) mill.
Mashing. This is mixing the malt with hot water (70oC) water, which infuses for an hour or so, and is then lautered (separating out the spent malt --- the infused water is the bit you want). You can use magic to heat the water and perhaps ReHe or ReAq to perform the separation. Maybe use magic to power a bore or something similar for the water supply.
Wort boiling and cooling. The infused water (wort) is usually transfered to another vessel and boiled for an hour or so, and then cooled down to near ambient temperature. During the boil hops (a herb flower) are added (which add some bitter flavours and act as a preservative). You can use magic to do the required heating and cooling, and to move the liquid from vessel to vessel.
Fermentation. The wort is transferred to another vessel, yeast is added into the wort, and it ferments away for a week or two. This requires cooling, as the fermentation releases heat. Temperature control might be done by magic. You could also use MuAq to magically ferment the wort.
Basically done. The yeast may need to be separated out (if you are worried about clarity) and you could put the finished beer into storage vessels. Some beers are stored for a while to develop other flavours.
Temperature control was not great in the medieval period --- because they couldn't measure it for a start.
Note, that it was not known until the 19th century that you needed to add yeast for fermentation to happen. Medieval brewers just accidentally infected their brews with ambient yeast (which is a mould). Which is one reason why regional beers were different, as there were different ambient yeasts. Keeping the brewery sterilised would actually be a bad idea, as you would kill the yeast. Of course, in Mythic Europe it might be a magic spirit/demon that governs the fermentation process.
Lots of other herbs were added in the 13th century instead of, or as well as, hops. Hops role as a preservative was not well understood. You can also cut the malt with other grains (like wheat, oats, etc) that haven't been malted. This is essentially what a wheat beer is, for example. This gives you a different flavour and appearence to the beer, and (importantly) is cheaper because you don't need to pay for as much malt.
Only if it is a sealed keg which you are filling. More a modern thing than an medieval issue.
The smoke flavour might be considered a feature rather than a problem.