A esteira e a bicicleta ergométrica estão aqui.

Because each noun has its own definite article:

• a esteira = the treadmill
• a bicicleta ergométrica = the exercise bike

In Portuguese, it is very normal to repeat the article with each noun in a list, especially when the nouns are specific items. English often does this too: the treadmill and the exercise bike.

Because the subject is plural.

The subject is:

• a esteira
• e
• a bicicleta ergométrica

That means the treadmill and the exercise bike = two things, so the verb must be plural:

• está = is
• estão = are

So:

• A esteira está aqui. = The treadmill is here.
• A esteira e a bicicleta ergométrica estão aqui. = The treadmill and the exercise bike are here.

Portuguese uses estar to talk about location:

• A esteira está aqui.
• Eles estão em casa.
• O livro está na mesa.

So estão aqui literally means are here in the sense of physical location.

Using ser here would be wrong. Ser is not the verb used for where something is located in this kind of sentence.

In Portuguese, adjectives usually come after the noun.

So:

• bicicleta ergométrica = exercise bike
• carro vermelho = red car
• casa grande = big house

Sometimes adjectives can come before the noun, but that usually changes the tone, style, or meaning. In this sentence, the normal order is noun + adjective.

Because it agrees with bicicleta, which is a feminine singular noun.

Agreement in Portuguese means the adjective changes to match the noun in gender and number:

• bicicleta ergométrica = feminine singular
• bicicletas ergométricas = feminine plural

Here, ergométrica describes only bicicleta, not esteira.

Yes. Both are feminine singular nouns, which is why they use a:

• a esteira
• a bicicleta

That grammatical gender is part of the noun itself. It does not mean the object is biologically female; it is just how the language classifies the word.

Not always. Esteira can mean different things depending on context.

Common meanings include:

• treadmill in a gym context
• mat
• conveyor belt

In this sentence, because it appears with bicicleta ergométrica, the gym meaning is the obvious one: treadmill.

Yes, it is a very common and natural term in Brazil.

You may also hear:

• bike in gym speech
• sometimes bicicleta estacionária

But bicicleta ergométrica is standard and very clear.

Aqui means here, usually near the speaker.

So estão aqui means are here.

Some related words are:

• aqui = here
• aí = there, near the person being spoken to
• ali / lá = there, over there

So if the objects are near the speaker, aqui is the natural choice.

In this sentence, keeping the articles is the most natural choice.

• A esteira e a bicicleta ergométrica estão aqui. = natural
• Esteira e bicicleta ergométrica estão aqui. = more telegraphic, less natural in ordinary speech

Portuguese often uses definite articles more than English does, especially when referring to specific things already known in the situation.

In Brazilian Portuguese, estão is pronounced roughly like es-TOWN, but with a nasal ending.

A few notes:

• the stress is on the last syllable: -tão
• ão is a nasal sound, very common in Portuguese
• it is not pronounced like a fully separate a + o

If you want a rough English-style guide, estão is approximately es-TAUNG, but nasalized.

Yes, in some contexts you can, but it changes the nuance.

• estão aqui = are here right now; simple location
• ficam aqui = stay/go here / are kept here / are located here as a more habitual or assigned place

So if you are just pointing out where they are, estão aqui is the best neutral choice.