El animal sigue vivo.

Here, sigue means continues to be or is still.

So El animal sigue vivo is literally something like The animal continues alive, which in natural English becomes The animal is still alive.

It comes from the verb seguir.

Because sigue is the conjugated form of the verb.

• seguir = the infinitive, to continue / to follow
• sigue = he/she/it continues or you continue (formal usted)

Since el animal is third person singular (it), Spanish uses sigue:

• El animal sigue vivo.

Because seguir can work as a kind of linking verb here.

Spanish often uses:

• seguir + adjective

to mean to remain / to still be.

So:

• está vivo = it is alive
• sigue vivo = it is still alive / it remains alive

You do not say sigue está vivo.

The difference is the idea of continuation.

• El animal está vivo = The animal is alive.
• El animal sigue vivo = The animal is still alive.

With sigue, the speaker suggests that this is surprising, important, or true despite time passing or despite expectations.

Yes. That is also natural Spanish.

• El animal sigue vivo
• El animal todavía está vivo

Both can mean The animal is still alive.

A small nuance:

• sigue vivo often stresses continuing in that state
• todavía está vivo often stresses still, up to now

In many situations, they are very close in meaning.

Because el means the.

So el animal means the animal, usually a specific animal already known from the context.

Compare:

• El animal sigue vivo. = The animal is still alive.
• Un animal sigue vivo. = An animal is still alive.

Using el suggests the speaker has a particular animal in mind.

Because vivo agrees with animal in number and, in this sentence, gender.

Here it is treated as singular masculine, so the adjective is vivo.

Compare:

• El animal sigue vivo. = singular
• Los animales siguen vivos. = plural
• La planta sigue viva. = feminine singular

So the ending changes to match the noun.

A simple pronunciation guide is:

• SEE-geh

A few helpful points:

• the u in gue is silent
• the stress is on the first syllable: SI-gue

So it sounds roughly like SEE-geh, not see-GOO-eh.

Because vivo is the normal everyday word for alive.

• vivo = alive
• viviente = living, but often more formal or technical

So:

• El animal sigue vivo sounds natural.
• El animal sigue viviente sounds odd or unnatural in normal conversation.

You will hear viviente more in expressions like:

• seres vivientes = living beings

Yes, very common.

It is used to say that a state continues:

• sigue abierto = it is still open
• sigue enfermo = he is still ill
• sigo cansado = I’m still tired
• siguen aquí = they are still here

So sigue vivo is part of a very useful and common structure.