Ten problem jest prostszy niż tamten.

Because problem is a masculine singular noun in the nominative case, and ten is the matching form of this for masculine nouns.

Polish demonstratives change to match the noun’s:

• gender
• number
• case

So:

• ten problem = this problem (masculine)
• ta książka = this book (feminine)
• to pytanie = this question (neuter)

Tamten means that one or that.

In this sentence, it stands for tamten problem = that problem, but Polish often leaves out the repeated noun when it is obvious from context.

So:

• Ten problem jest prostszy niż tamten. literally = This problem is simpler than that one.

In Polish, problem is a masculine noun. Many masculine nouns end in a consonant, and problem follows that pattern.

So in the nominative singular:

• ten problem
• ten dom
• ten student

This is something you mainly have to learn with the noun, because grammatical gender in Polish does not always match what an English speaker might expect.

Prostszy is the comparative form of prosty.

• prosty = simple / straightforward
• prostszy = simpler

This is one of the common Polish comparative patterns where the adjective changes form rather than using a separate word like English more.

So:

• prosty → prostszy
• młody → młodszy
• tani → tańszy

You do not need to predict every stem change perfectly at first; many comparatives simply need practice and exposure.

You usually use prostszy, because it is the normal, natural comparative form.

• prosty = simple
• prostszy = simpler

Bardziej prosty is grammatically understandable, but it sounds less natural in ordinary Polish. In many cases, Polish prefers the single-word comparative when one exists.

Niż means than in comparisons.

So:

• prostszy niż tamten = simpler than that one

It is the standard word used after a comparative adjective:

• większy niż... = bigger than...
• lepszy niż... = better than...
• trudniejszy niż... = more difficult than...

Yes, very often you can.

With od, the second part changes to the genitive:

• Ten problem jest prostszy niż tamten.
• Ten problem jest prostszy od tamtego.

Both mean the same thing: This problem is simpler than that one.

A useful rule:

• niż
  • the basic comparison form you see here
• od
  • genitive

So:

• niż tamten
• od tamtego

In niż tamten, tamten is in the nominative form.

That often surprises English speakers, especially if they already know that od requires the genitive.

Compare:

• niż tamten → nominative form
• od tamtego → genitive form

So the sentence keeps:

• ten problem
• tamten

both in nominative-looking forms.

Yes, in a normal full sentence like this, jest is the standard and natural form.

• Ten problem jest prostszy niż tamten. = correct, normal

Leaving it out would usually sound unnatural in everyday standard Polish:

• Ten problem prostszy niż tamten. = not normal as a regular sentence

So for learners, the safe rule is: with this kind of sentence, keep jest.

Yes, Polish word order is fairly flexible, but the most neutral version is:

• Ten problem jest prostszy niż tamten.

Other orders are possible for emphasis, for example:

• Prostszy jest ten problem niż tamten.
• Ten problem prostszy jest niż tamten.

But these sound marked, literary, or strongly emphatic. For ordinary use, stick with the original order.

Because Polish often avoids repeating a noun when the meaning is already clear.

So instead of saying:

• Ten problem jest prostszy niż tamten problem

Polish normally says:

• Ten problem jest prostszy niż tamten

This works just like English that one, where one replaces the repeated noun.

No. Prosty can mean different things depending on context, including:

• simple
• straight
• plain
• straightforward

In this sentence, with problem, it means simple / easier to deal with, not physically straight.

So:

• prosta linia = a straight line
• prosty problem = a simple problem

It can look intimidating because of the consonant cluster.

A rough guide is:

• prostszy ≈ PROST-shih

The important part is that sz sounds like English sh.

So the word breaks roughly like:

• prost-szy

You do not need a perfect English-style approximation, but recognizing sz = sh is very helpful.