A múlt és a jelen különböző.

Because Hungarian usually omits the verb to be in the present tense, third person when the predicate is a noun or an adjective.

So:

• A múlt és a jelen különböző.
• literally: The past and the present different.
• natural English: The past and the present are different.

If you change the tense, Hungarian does use the verb:

• A múlt és a jelen különbözőek voltak. = The past and the present were different.

A is the definite article, meaning the.

Hungarian normally repeats the article before each coordinated noun when both are definite:

• a múlt és a jelen = the past and the present

Also, Hungarian has two forms of the definite article:

• a before a consonant sound
• az before a vowel sound

Since múlt and jelen both begin with consonant sounds, a is used both times.

Yes. In this sentence, both are nouns:

• múlt = past
• jelen = present

They can sometimes appear in other roles depending on context, but here they are clearly the two nouns forming the subject of the sentence.

It is an adjective, meaning different.

So the structure is basically:

• A múlt és a jelen = subject
• különböző = predicate adjective

Hungarian could also express a similar idea with a verb such as különbözik (to differ), but this sentence does not use a verb of that kind. It uses the adjective különböző.

That is a very normal Hungarian word order.

In a neutral sentence, Hungarian often puts:

• the topic first
• the new information/comment after it

So here:

• A múlt és a jelen = what we are talking about
• különböző = what is being said about them

You can change the order for emphasis, but the given order is the most straightforward and neutral one.

This is a very reasonable question, because learners often expect a plural-looking predicate with a compound subject.

In practice, különböző without the plural ending is very common and natural in short, abstract statements like this. You may also hear különbözőek.

So:

• A múlt és a jelen különböző.
• A múlt és a jelen különbözőek.

Both can be encountered. The version in your sentence is perfectly idiomatic and feels compact and general.

Because it does not need to.

Once the two things being compared are already named, Hungarian can simply say különböző and leave the comparison understood.

English often likes to make that relationship more explicit, but Hungarian is comfortable leaving it implicit here.

If you want to spell it out more clearly in Hungarian, you can use another structure, for example:

• A múlt különbözik a jelentől. = The past differs from the present.

But in your sentence, that extra wording is unnecessary.

Yes, absolutely. In Hungarian, accent marks are part of the spelling and they affect pronunciation.

For example:

• u and ú are different vowels
• o, ö, and ő are different vowels
• e and é are different vowels

So you should learn the words with their accents exactly as written:

• múlt
• és
• különböző

They are not optional decoration.

A few useful points:

• Hungarian s is pronounced like English sh
• Hungarian stress is usually on the first syllable of each word

So:

• és sounds roughly like aysh with a long vowel
• különböző begins with front rounded vowels ü and ö/ő, which are unfamiliar to many English speakers

A rough guide:

• különböző ≈ KÜ-lön-bö-ző
• stress on the first syllable: KÜ...

If you know German or French, the rounded vowels may feel more familiar:

• ü is somewhat like German ü
• ö / ő are somewhat like German ö or French rounded vowels

In normal prose, a múlt és a jelen is the standard way to say the past and the present.

Leaving out the articles might sound more like:

• a heading
• a title
• a poetic or compressed style

So for an ordinary full sentence, keep the articles:

• A múlt és a jelen különböző.