Eu gosto de assistir à televisão à noite, mas quase nunca lembro o número do canal.

Because gostar normally requires the preposition de.

So Portuguese says:

• gostar de + noun
• gostar de + infinitive

Examples:

• Gosto de música.
• Gosto de estudar.
• Gosto de assistir à televisão.

A literal word-for-word version would be something like I like of watching, but in natural English we just say I like watching.

In standard Portuguese, when assistir means to watch, it normally takes the preposition a.

So:

• assistir a + a televisão = assistir à televisão

That à is the contraction of:

• a = the preposition required by assistir
• a = the feminine singular article before televisão

So à here is a case of crase.

Important note for Brazilian Portuguese:

• In everyday speech, many Brazilians do say assistir televisão or especially assistir TV
• But the more traditional standard form is assistir à televisão

Yes. Both are very common in Brazil.

Some common options are:

• ver televisão
• ver TV
• assistir à televisão
• assistir TV

In everyday Brazilian Portuguese, ver TV and assistir TV are extremely natural.

Very roughly:

• ver is often the most casual and common
• assistir sounds a little more formal or careful, especially in writing

Here à noite means at night or in the evening / at night, depending on context.

This is another case of crase. In time expressions, Portuguese often uses a + feminine noun/article, which becomes à.

So:

• à noite = at night
• à tarde = in the afternoon
• à meia-noite = at midnight

This à is not related to assistir. It is part of the time expression.

You can omit Eu if the context is clear:

• Eu gosto de assistir à televisão à noite...
• Gosto de assistir à televisão à noite...

Both are correct.

In Brazilian Portuguese, subject pronouns are used more often than in European Portuguese, but they are still often omitted when the verb form already makes the subject clear.

Using Eu can:

• make the subject more explicit
• add emphasis
• sound slightly more natural at the beginning of a standalone sentence

Quase nunca means almost never or hardly ever.

It is made of:

• quase = almost
• nunca = never

So literally it is almost never.

Examples:

• Eu quase nunca saio à noite.
• Ela quase nunca come carne.

It is a very common expression in Portuguese.

This is a very good question, because both patterns exist.

With lembrar, Portuguese can use different constructions:

1. lembrar algo

   • Lembro o número.
   • direct object

2. lembrar-se de algo

   • Me lembro do número.
   • pronominal form with de

In Brazilian Portuguese, many speakers very often say:

• não lembro do número
• não me lembro do número

So the version in your sentence, lembro o número, is correct, but in everyday Brazilian speech, me lembro do número or lembro do número may sound more common to many people.

Do is the contraction of:

• de + o = do

So:

• o número do canal = the number of the channel

Portuguese very often combines prepositions with articles:

• de + o = do
• de + a = da
• em + o = no
• em + a = na
• a + a = à

Portuguese usually expresses this idea with a structure like:

• the number of the channel
• o número do canal

This is more natural in Portuguese than copying the English noun-noun structure.

Other similar examples:

• a porta da casa = the door of the house
• o nome da rua = the name of the street
• o fim do filme = the end of the movie

So o número do canal is the normal Portuguese way to say the channel number.

Yes. Televisão is the full word, and TV is the shorter everyday form.

In Brazil, TV is extremely common in speech:

• Vou assistir TV.
• O que está passando na TV?

The full form televisão is also completely normal, but it can sound a bit more formal or simply more complete.

They are very close, and in Brazil both are common.

• à noite is often felt as a bit more neutral or standard
• de noite is very common in everyday speech

Examples:

• Eu estudo à noite.
• Eu estudo de noite.

Both are natural in Brazilian Portuguese.

Yes. Mas is the normal word for but in Portuguese.

In your sentence, it connects two contrasting ideas:

• I like watching television at night
• but I almost never remember the channel number

So:

• ..., mas quase nunca lembro...

This works very much like English but.