O gerador dá eletricidade ao hospital.

Because gerador is a masculine singular noun in Portuguese.

• o = the for masculine singular nouns
• gerador = generator

So o gerador means the generator.

Dá is the 3rd person singular present tense of dar (to give):

• eu dou = I give
• tu dás = you give
• ele/ela dá = he/she/it gives

The accent in dá shows the stressed vowel and also helps distinguish it from da, which is a different word: the contraction of de + a.

So:

• dá = gives
• da = of/from the (feminine singular)

Because a + o contracts to ao in Portuguese.

Here:

• a = to
• o hospital = the hospital
• a + o hospital → ao hospital

This contraction is mandatory in standard Portuguese.

Other similar contractions are:

• a + a → à
• a + os → aos
• a + as → às

In Portuguese, hospital normally takes the definite article in this kind of sentence, especially in European Portuguese.

So the natural form is:

• ao hospital = to the hospital

Leaving the article out would sound unusual in most ordinary contexts.

With dar, the normal pattern is:

dar alguma coisa a alguém = to give something to someone

So:

• O gerador dá eletricidade ao hospital.
• literally: The generator gives electricity to the hospital.

Using para would not be the normal basic structure with dar for the recipient.

A good rule is:

• dar + thing + a + recipient

Because eletricidade is being used as a mass noun in a general sense, like water, money, or energy.

So Portuguese often says:

• dar eletricidade
• fornecer água
• produzir energia

If you added an article, it would usually make the noun more specific:

• dá a eletricidade do gerador ao hospital = gives the electricity from the generator to the hospital

But in your sentence, the general idea is simply gives electricity.

Yes. It is the most natural neutral order.

The structure is:

• O gerador = subject
• dá = verb
• eletricidade = direct object
• ao hospital = indirect object / recipient

So the pattern is:

subject + verb + thing + recipient

That is very common with dar.

Yes. That is also correct, and in many contexts it may even sound more natural.

• dar eletricidade = give electricity
• fornecer eletricidade = supply electricity

Fornecer is often a bit more technical or formal.
Dar is simpler and very understandable.

So both work, but fornece eletricidade may sound more like the usual phrasing in technical or practical contexts.

A rough guide is:

u zhuh-ruh-DOR dah ee-leh-tree-see-DAD ao osh-pee-TAL

A few important points:

• O before a consonant is usually pronounced like a weak u sound.
• gerador has the main stress on the last syllable: -dor
• dá is clearly stressed
• h in hospital is silent
• hospital is stressed on the last syllable: tal

European Portuguese reduces many unstressed vowels, so it may sound more compressed than the spelling suggests.

You use lhe, because hospital is the indirect object here.

So:

• O gerador dá eletricidade ao hospital.
• O gerador dá-lhe eletricidade.

Here lhe means to it / to the hospital.

This is a very useful pattern:

• dar algo a alguém
• dar-lhe algo

In European Portuguese, this kind of indirect-object pronoun is very common.

In this sentence, it means to the hospital, because it is the recipient of dar.

With dar, a alguém/algo marks who receives something.

So here:

• eletricidade = what is given
• ao hospital = who receives it

If you wanted to say at the hospital, Portuguese would normally use no hospital:

• Há um gerador no hospital. = There is a generator at/in the hospital.

So:

• ao hospital = to the hospital
• no hospital = in/at the hospital

No problem at all. Portuguese often uses dar with non-human subjects when something provides or produces an effect.

So a machine can:

• dar eletricidade
• dar energia
• dar problemas
• dar calor

This is perfectly natural. It does not mean the generator is acting like a person; it is just a normal way to express that it provides something.