אהבה לכלב חשובה.

A natural pronunciation is:

• ahavá lekelev chashuvá = love for a dog is important
• ahavá lakelev chashuvá = love for the dog is important

The difference is in לכלב:

• לְכֶלֶב = lekelev = to/for a dog
• לַכֶּלֶב = lakelev = to/for the dog

In unpointed Hebrew, both are written the same: לכלב.

Because Hebrew often combines the preposition ל־ (to/for) with the definite article ה־ (the).

So:

• ל + כלב → לכלב = to/for a dog
• ל + הכלב → לכלב = to/for the dog

Without vowel marks, the spelling is identical. Context usually tells you which one is meant.

Because חשובה is feminine singular, and it agrees with אהבה, which is a feminine singular noun.

• אהבה = feminine singular
• so the adjective is חשובה = feminine singular

If the subject were masculine singular, you would use חשוב instead.

Because the main thing being described is אהבה (love), not כלב (dog).

The structure is basically:

• אהבה לכלב = love for a/the dog
• חשובה = is important

So the sentence says that the love is important. Since אהבה is feminine, the adjective is feminine too.

In present-tense Hebrew, is/am/are is usually omitted.

So:

• אהבה לכלב חשובה literally looks like:
• love for a/the dog important

but it means:

• Love for a/the dog is important

This is completely normal Hebrew.

Because Hebrew uses ל־ here to mark the target of the feeling: love for/toward a dog.

So:

• אהבה לכלב = love for a dog / love toward a dog

By contrast, אהבה כלב would not be normal Hebrew.

Also note the difference between the noun and the verb:

• אהבה לכלב = love for a dog
• לאהוב כלב = to love a dog

With the noun אהבה, the ל־ phrase is natural.

Because את marks a definite direct object of a verb, and this sentence does not have that kind of structure.

Here:

• אהבה is a noun
• לכלב is a prepositional phrase with ל־

So את does not belong here.

Compare:

• אני אוהב את הכלב = I love the dog
  Here את is used because הכלב is the definite direct object of the verb אוהב.

But in:

• אהבה לכלב חשובה

there is no direct object marked by את.

It means love directed toward a dog/the dog, not the dog’s love.

If you want to say the dog’s love or a dog’s love, you would use a different structure, such as:

• אהבת הכלב = the dog’s love
• אהבה של הכלב = the love of the dog

So:

• אהבה לכלב = love for the dog
• אהבת הכלב = the dog’s love

Those are different ideas.

Not in the most natural reading.

אהבה לכלב חשובה is most naturally understood as:

• Love for a/the dog is important

If you want to say:

• Love is important to the dog

the more natural word order would be:

• אהבה חשובה לכלב

That puts לכלב with important to the dog, instead of with love for the dog.

Yes. This is a normal kind of Hebrew sentence:

• [subject phrase] + [predicate adjective]

Here:

• אהבה לכלב = the subject phrase
• חשובה = the predicate adjective

So the order is natural and clear.

It is ambiguous in unpointed Hebrew.

Because לכלב can be read either as:

• for a dog or
• for the dog

So the sentence could mean either:

• Love for a dog is important or
• Love for the dog is important

If the writer wants to make it clearer, they might add context or extra words, for example:

• אהבה לכלב הזה חשובה = Love for this dog is important
• אהבה לכלב כלשהו חשובה = Love for some dog / a certain dog is important