هذه وجهة جديدة.

Because وجهة is a feminine noun in Arabic.
Arabic this must agree with the gender of the noun:

• هذا = this for masculine nouns
• هذه = this for feminine nouns

So:

• هذا كتاب = This is a book
• هذه وجهة = This is a destination

A common clue is the ending ة, which often marks a feminine noun.

In Arabic, the verb to be is usually not written or spoken in the present tense in sentences like this.

So هذه وجهة جديدة literally looks like:

• this + destination + new

but it means:

• This is a new destination

This kind of sentence is very common in Arabic.

Arabic does not have a separate word for the indefinite article a/an.

Instead, indefiniteness is usually shown by context, and in fully vowelled Arabic by tanwīn:

• وِجْهَةٌ = a destination
• جَدِيدَةٌ = new in an indefinite form agreeing with the noun

So وجهة جديدة means a new destination, even though there is no separate word for a.

Because in Arabic, adjectives normally come after the noun they describe.

So Arabic says:

• وجهة جديدة
• literally: destination new

but in English we say:

• new destination

This is the normal word order for noun + adjective in Arabic.

Because the adjective must agree with the noun it describes.

Since وجهة is:

• feminine
• singular
• indefinite

the adjective must also be:

• feminine
• singular
• indefinite

Compare:

• كتاب جديد = a new book
• وجهة جديدة = a new destination

So جديد becomes جديدة to match the feminine noun.

Good question. There are two different patterns here.

1. Demonstrative + definite noun
   This makes a noun phrase:

• هذه الوجهة الجديدة = this new destination

2. Demonstrative used by itself + an indefinite predicate
   This makes a full sentence:

• هذه وجهة جديدة = This is a new destination

So in your sentence, هذه is standing on its own as this, and وجهة جديدة is the rest of the sentence.

A careful MSA pronunciation is:

hādhihi wijhatun jadīdatun

In normal pause, many speakers simplify the endings, so you may hear something closer to:

hādhihi wijha jadīda

A few notes:

• هذه = hādhihi
• وجهة = wijha in pause, wijhatun with full case ending
• جديدة = jadīda in pause, jadīdatun with full case ending

The final ة is often pronounced like -a in pause.

It would be:

هٰذِهِ وِجْهَةٌ جَدِيدَةٌ

Those final ـٌ endings are called tanwīn. Here they show that وجهة and جديدة are:

• indefinite
• nominative

In everyday writing, these short vowels are usually omitted, so you normally just see:

هذه وجهة جديدة

It is a nominal sentence in Arabic.

You can think of it like this:

• هذه = the subject/topic, this
• وجهة جديدة = the predicate, a new destination

So the structure is:

• This + [is] + a new destination

This is one of the most common sentence types in Arabic.