Learn Portuguese (Portugal): Eles têm boas profissões.

Most Portuguese words ending in -ão form their plural by changing to -ões. The singular is profissão and the plural is profissões. While there are a few words that change to -ãos or -ães, -ões is by far the most common pattern, especially for words ending in -ção or -ssão.

Why is the feminine adjective boas used with profissões?

Because profissão is a feminine noun. As a very helpful rule of thumb, almost all Portuguese nouns ending in -ção or -ssão (like profissão, informação, or televisão) are feminine. Therefore, the adjective must match it and become the feminine plural boas.

Why does têm have a circumflex accent (the "little hat")?

The accent tells you this is the plural form, meaning "they have". The singular form ele tem (he has) has no accent, while the plural form eles têm (they have) gets the circumflex to show the difference in grammar.

Doesn't the adjective usually go after the noun? Why is it boas profissões here?