Learn Spanish (Latin America): El señor este es muy fastidioso.

Placing the demonstrative (este) after the noun, accompanied by the definite article (el), adds a strong emotional tone. Here, it sounds dismissive, exasperated, or derogatory, similar to saying 'this guy' or 'this particular man' in English when you are complaining.

Can I use other demonstratives after the noun, like in El señor ese?

Absolutely. You can use ese or aquel in the exact same way. In fact, El señor ese is extremely common when you want to distance yourself from the person or express contempt, translating roughly to 'that guy'.

Is fastidioso a false friend? Does it mean 'fastidious' (fussy or strictly attentive to detail)?

Yes, it is usually a false friend. While it can sometimes mean fussy, in Latin American Spanish, fastidioso almost always means 'annoying', 'bothersome', or 'irritating'.

Why use es rather than está here?

Using es (from ser) tells us that being annoying is an ongoing personality trait of this man. If you used está (from estar), it would mean he is just acting annoying right now in this specific moment.