Learn Dutch: Drink jij bier zonder alcohol? - Are you drinking beer without alcohol?

You could use the suffix -vrij (meaning free of) and say Drink jij alcoholvrij bier?. In fact, alcoholvrij bier is the most natural and common way to refer to alcohol-free beer in Dutch.

What if the beer has a little bit of alcohol in it, rather than none at all?

In that case, you would use the suffix -arm (meaning low or poor in). You would ask Drink jij alcoholarm bier? which translates to low-alcohol beer.

Could I use -rijk with alcohol to describe a strong drink?

Yes, you can use alcoholrijk to describe a drink with a high percentage of alcohol. For example, you might say Dat is een alcoholrijk bier (That is a strong/alcohol-rich beer).

Why doesn't the verb have a -t at the end, like Drinkt jij?

Remember the inversion rule: when the subject jij or je comes immediately after the verb, the verb drops the -t. If it were a statement, it would be Jij drinkt, but as a question, it becomes Drink jij.