So my answer to this question is mostly sourced from the book " The Time Travellers Guide to Medieval England" and my own experiences with fermenting drinks.

In the Medieval period there wasn't really much beer to be had in most of Europe until well after 1400. Due to the simplicity of the recipe and availability of the ingredients most people made ale at home. It's basically just boiled cereal juice with yeast added for fermentation which made it easier to come by as well as cheaper than bread.

It wasn't so much regarded as an alcoholic drink as it was "liquid bread". It might've also contained debris of the crushed boiled grains (why throw out those extra calories?) making it resemble a very thin fermented gruel.

Medieval ale usually wouldn't have been as strong as what we know as beer or ale because it was usually consumed within 2-3 days. In that time you'd be hard pressed to get it to more than 1 or maybe 2% alcohol by volume, depending on the yeast, temperature and a million other factors. So letting children drink it wasn't as big a deal as some people might think.

The quality and taste could best be described as "varying widely".

Back then there was no estrablished yeast strains so even if you used some of your old batch to start a new one it'd probably catch some wild yeasts somewhere in the process. If you've ever done a wild ferment you'll know that there's a good chance your brew might develop some off-flavours like ammonia, especially if it's already a few days old. Since there was no filtering, refrigeration or pasteurization available, let alone sterile and airtight storage vessels ale would stay good for a week at most, at which point it would've started souring and required the addition of spices or some sweetener to remain palatable. Live drinks will continue developing over time unless pasteurized so I think people would've had differing preferences how mature they liked their ale.

Because of how easy ale is to make there'd always be a household nearby with a fresh batch so most people would buy it from their neighbors or an alehouse if none was available in their own home.

Since no sturdy airtight containers were available it also would've been a flat drink with no carbonation. Overall I doubt it'd be overly pleasant-tasting to someone used to modern bottled brews. Probably not terrible once you get used to the different, less "clean" taste and texture.

I've made Kvass (basically a slavic sweet rye bread-based light ale) Ginger beer and fermented Water Kefir before and they all tend to develop this slightly rough, yeasty quality if you let them sit unrefrigerated for more than 2 days, and that does take some getting used to. Since I didn't want to waste what I'd made I drank it anyways, didn't do me any harm and in the end I barely tasted the slight unpleasantness any more.

If you're curious (and over the legal drinking age where you live) I encourage you to just get some unprocessed grains and a few large mason jars, make a wild yeast starter and try it for yourself. This is something you can easily experience without a time machine 😉