הפגוש שחור.

It is the Hebrew definite article, equivalent to the in English.

So:

• פגוש = bumper
• הפגוש = the bumper

In simple present-tense Hebrew sentences, the verb to be is usually omitted.

So הפגוש שחור literally looks like the bumper black, but it means the bumper is black.

In other tenses, Hebrew does use a word for was / will be, for example:

• הפגוש היה שחור = the bumper was black
• הפגוש יהיה שחור = the bumper will be black

Because these are two different structures:

• הפגוש שחור = a full sentence: the bumper is black
• הפגוש השחור = a noun phrase: the black bumper

When the adjective is part of the noun phrase, it usually matches the noun in definiteness, so both words take ה־.

When the adjective is the predicate of the sentence, as in הפגוש שחור, it normally does not take ה־.

In Hebrew, adjectives normally come after the noun.

So Hebrew says:

• פגוש שחור = black bumper / a black bumper

not the English-style order black bumper.

The same after-the-noun pattern also appears in simple sentences like הפגוש שחור.

Because it agrees with פגוש, which is masculine singular.

שחור is the masculine singular form of black.

Other forms are:

• שחורה = feminine singular
• שחורים = masculine plural
• שחורות = feminine plural

For example:

• המכונית שחורה = the car is black
• הפגושים שחורים = the bumpers are black

Yes, but the meaning changes.

• פגוש שחור usually means a black bumper
• הפגוש שחור means the bumper is black

So the ה־ is important. It tells you that the noun is definite: the bumper, not just a bumper.

A common way is:

• הפגוש לא שחור = the bumper is not black

You may also see the more formal style:

• הפגוש אינו שחור

Both mean the same thing, but לא is the simpler and more everyday pattern for many learners to start with.