O relógio funciona bem.

In Portuguese, we often use the definite article (o, a) even when talking about something in general.

• O relógio literally means “the watch.”
• If you want to say “a watch,” you use the indefinite article um: Um relógio funciona bem (“A watch works well”).
  However, general truths in Portuguese usually prefer the definite article—so O relógio funciona bem sounds more natural when you mean “watches work well” in general.

Portuguese nouns have grammatical gender. Relógio ends in -o, which often (though not always) signals a masculine noun. That’s why it takes o as its article.
Tips for guessing gender:

• Many nouns ending in -o are masculine; those ending in -a are feminine.
• There are exceptions, so a dictionary check is safest.

Relógio is pronounced roughly [ʁɨˈlɔ.ʒu] in European Portuguese. Key points:

• The stress falls on the second syllable: ló.
• The é in relógio is pronounced like the “e” in “bed,” but closed.
• The gl before i often sounds like [ʒ] (similar to the “s” in “measure”).

Funcionar means “to function” or “to work” (in the sense of operating). It’s the standard verb for machines, devices or systems:

• O computador funciona (“The computer works”).
  Trabalhar is used for people or living beings doing work, e.g., Eu trabalhei (“I worked”).

Yes, but in European Portuguese the present simple often covers both “works” and “is working.” If you want a continuous feel, you use:

• O relógio está a funcionar bem (literally “is at functioning well”).
  Still, O relógio funciona bem is perfectly natural even if you mean right now.

No. Funcionar is intransitive, so it doesn’t take a direct object. You simply say funcionar bem.
If you want to specify conditions or tools, use a prepositional phrase:

• O relógio funciona com pilha nova (“The watch works with a new battery”).

Yes, Portuguese often omits the subject because the verb ending shows person/number. Funciona already implies “it/he/she works.” But in a standalone sentence, learners usually keep o relógio for clarity. In a clear context you’ll hear:

• (—How’s the printer?)
• Funciona bem.