Learn Portuguese (Portugal): A droga é um problema nesta cidade.

In Portuguese, it is very common to use the singular a droga as an uncountable mass noun to talk about drugs in general, or the issue of drug use. You can say as drogas, but the singular form is the most natural choice for general statements like this one.

Why is it um problema and not uma problema?

Problema is a masculine word, despite ending in "-a". This is a common exception to the general rule. Many Portuguese words that end in "-ma" (especially those with Greek origins, like o sistema, o programa, and o tema) are masculine and take the masculine article um.

Could I use nessa cidade instead of nesta cidade?

It depends on where you are! Nesta is a contraction of em + esta (in this) and implies the speaker is currently in the city they are talking about. If you were talking to someone about their city, or a city you just mentioned but aren't currently in, you would use nessa (in that).

Why do we use é here instead of está, if the problem might eventually be fixed?

When you equate one noun with another to define what it is (here, saying that "drugs" is "a problem"), you must use the verb ser (é). The verb estar is used for temporary states or locations, but not for defining what a thing fundamentally is.