Mi hermana es ambiciosa y muy trabajadora, pero no olvida descansar ni cuidar su salud.

Because ambiciosa and trabajadora describe general personal qualities, not temporary states.

• ser is used for identity, profession, character, and lasting traits.
• estar is used for states, conditions, and locations.

So:

• Mi hermana es ambiciosa = my sister is ambitious
• Mi hermana es trabajadora = my sister is hardworking

Using está here would sound wrong unless you were describing a temporary condition, which these adjectives normally are not.

They change to match hermana, which is feminine singular.

In Spanish, many adjectives agree in gender and number with the noun they describe.

• hermano → ambicioso, trabajador
• hermana → ambiciosa, trabajadora

If the sentence were about a brother, it would be:

• Mi hermano es ambicioso y muy trabajador.

Because muy is used to modify adjectives and adverbs.

• muy trabajadora = very hardworking

Mucho/a/os/as is used with nouns, or as a pronoun/adverb in other contexts:

• mucho trabajo = a lot of work
• trabaja mucho = she works a lot

So here, since trabajadora is an adjective, muy is the correct word.

Here it means hardworking.

Although trabajador/trabajadora can sometimes refer to a worker as a noun, in this sentence it is clearly an adjective describing your sister’s personality.

So:

• Mi hermana es trabajadora = My sister is hardworking

If it were a noun, the structure would usually make that clearer, for example:

• Mi hermana es una trabajadora excelente = My sister is an excellent worker

In Spanish, it is normal to put a comma before pero when it joins two clauses with contrasting ideas.

Here the contrast is:

• she is ambitious and hardworking, but
• she does not forget to rest or take care of her health

So the comma helps separate those two connected ideas clearly.

Because olvidar can be followed directly by an infinitive when it means to forget to do something.

So:

• olvidar + infinitive
• olvida descansar = she forgets to rest
• no olvida descansar = she doesn’t forget to rest

You do not use de here.

Compare:

• Olvidé cerrar la puerta. = I forgot to close the door.
• No olvides llamar. = Don’t forget to call.

Because they are the actions linked to olvida.

After olvidar, Spanish often uses the infinitive to express what someone forgets or remembers to do:

• olvida descansar
• olvida cuidar su salud

This is similar to English forget to rest / forget to take care of her health.

So the structure is:

• no olvida + infinitive + ni + infinitive

Here ni means nor.

In a negative sentence, Spanish often uses ni to link two negative or negated items:

• no olvida descansar ni cuidar su salud

Literally, this is like:

• she does not forget to rest, nor to take care of her health

In natural English, you would usually say:

• she doesn’t forget to rest or take care of her health

So ni is the natural Spanish choice after no in this structure.

Because Spanish usually prefers a possessive adjective like su when the owner is clear from context.

Here, su salud naturally refers to her sister’s health.

• cuidar su salud = to take care of her health

You could say la salud de ella, but that is usually more emphatic, more explicit, or used only if there could be confusion.

Spanish often uses possessives more economically than English does.

Not always. It depends on context.

Like English ambitious, ambicioso/a can be:

• positive: motivated, goal-oriented
• negative: overly driven, ruthless, too focused on success

In this sentence, because it is paired with muy trabajadora and balanced with no olvida descansar ni cuidar su salud, it sounds mostly positive.

So here it suggests someone who has goals and works hard, but in a healthy way.

Normally, no.

For a person’s usual character trait, Spanish uses ser:

• Mi hermana es muy trabajadora.

Using estar trabajadora is not standard in this context. A native speaker would expect ser with this adjective when describing someone as hardworking in general.

It suggests that, despite being ambitious and hardworking, she still remembers to rest and look after herself.

It does not simply mean she has a good memory. It means she doesn’t neglect those things.

So the idea is something like:

• she works hard, but she still makes time to rest
• she is careful not to ignore her health

This is a very natural way in Spanish to express a balanced habit or attitude.

Yes, but it would change the structure slightly.

For example:

• Mi hermana es ambiciosa y muy trabajadora, sin olvidar descansar ni cuidar su salud.

However, this version sounds less natural than the original in many everyday contexts.
The original:

• pero no olvida descansar ni cuidar su salud

is clearer and more straightforward.

So while sin olvidar is possible in some contexts, the sentence as given is the more natural choice for ordinary speech and writing.