Learn Portuguese (Portugal): O talho fecha à segunda-feira.

In Portuguese, you can indicate a recurring, habitual event by using the preposition a (contracted to à) with the singular day of the week. While you can also say às segundas-feiras, using the singular form is very common and perfectly natural for expressing "every Monday."

Would it be wrong to say na segunda-feira in this context?

Yes, it would change the meaning. Using the preposition em (contracted to na) usually refers to one specific occurrence, like "next Monday" or "last Monday." Because a shop's closing schedule is a weekly routine, you must use à to show that it happens regularly.

In everyday speech, do I always need to include the word feira?

Not always. In casual conversation, Portuguese speakers frequently drop it and simply say à segunda. However, for official information like a shop's business hours, using the full name segunda-feira is the standard.

Does o talho mean the butcher shop or the butcher as a person?

O talho specifically refers to the butcher shop. If you are talking about the person who cuts and sells the meat, the standard European Portuguese word is o talhante.