Muszę przyznać, że ten sernik jest pyszny.

Muszę is the 1st person singular present form of the verb musieć.

So:

• musieć = the dictionary form, to have to / must
• muszę = I have to / I must

This is a normal Polish pattern: after you look up a verb in the infinitive, you usually have to conjugate it to match the subject.

For musieć, the present-tense forms are:

• muszę = I must
• musisz = you must
• musi = he/she/it must
• musimy = we must
• musicie = you all must
• muszą = they must

So Muszę przyznać... starts with I must admit...

Because after muszę, Polish normally uses an infinitive.

The pattern is:

• muszę + infinitive
• chcę + infinitive
• mogę + infinitive

Examples:

• Muszę iść = I must go
• Chcę spać = I want to sleep
• Mogę zostać = I can stay

So:

• muszę przyznać = I must admit

You do not say muszę przyznaję. That would mix two finite verb forms, which is not how this structure works.

This is an aspect question.

Polish verbs often come in pairs:

• przyznawać = imperfective
• przyznać = perfective

Here, przyznać is used because the speaker means one complete act of admitting something. That is the natural choice in a sentence like this.

So Muszę przyznać is the normal, idiomatic way to say I have to admit.

If you used przyznawać, it would suggest something more ongoing, repeated, or incomplete, which does not fit this sentence well.

Że introduces a subordinate clause. In this sentence, it works like English that.

Structure:

• Muszę przyznać = I must admit
• że ten sernik jest pyszny = that this cheesecake is delicious

So że connects the two parts of the sentence.

English often drops that:

• I must admit this cheesecake is delicious.

Polish usually keeps że in this kind of sentence.

Because in Polish, a comma before że is normally required.

Polish punctuation is stricter than English here. When że introduces a subordinate clause, you separate it with a comma:

• Muszę przyznać, że...

This is standard written Polish.

Because sernik is a masculine singular noun, and ten must agree with it.

Here:

• ten = masculine singular nominative
• sernik = masculine singular nominative

They match in:

• gender
• number
• case

This is the same agreement pattern you see elsewhere in Polish:

• ta kawa = this coffee, feminine
• to ciasto = this cake, neuter

In your sentence, ten sernik is the subject of jest, so it is in the nominative case.

Usually ten means this, but in real usage it can also feel a bit like this particular or even help mark something as already identified in context.

Polish has no articles like a or the, so words like ten sometimes do extra work.

Compare:

• Sernik jest pyszny = Cheesecake is delicious / The cheesecake is delicious
• Ten sernik jest pyszny = This cheesecake is delicious / This particular cheesecake is delicious

So adding ten makes the noun more specific.

Because adjectives in Polish must agree with the noun they describe.

Here the noun is:

• sernik = masculine singular nominative

So the adjective must also be:

• pyszny = masculine singular nominative

Compare:

• ten sernik jest pyszny = masculine
• ta kawa jest pyszna = feminine
• to ciasto jest pyszne = neuter

Even though pyszny comes after jest, it still agrees with sernik.

Yes, in normal standard Polish, jest is the natural and expected form here.

• ten sernik jest pyszny = standard, complete sentence

Polish does not usually drop the present-tense form of to be in ordinary sentences like this.

So learners should definitely keep jest.

Yes. Polish word order is more flexible than English, because endings carry a lot of grammatical information.

Your sentence:

• Muszę przyznać, że ten sernik jest pyszny.

This is a very natural, neutral order.

Other orders are possible, but they change the emphasis:

• Ten sernik jest pyszny, muszę przyznać.
  Focuses more on the cheesecake
• Muszę przyznać, że pyszny jest ten sernik.
  More marked, more stylistic

For learners, the original version is the safest and most natural choice.

A few sounds here are especially important:

• sz in muszę and pyszny sounds like English sh
• ż / rz in że sounds like the s in measure
• ć in przyznać is a soft consonant, somewhat like a softer version of ch
• y in pyszny is not the English ee sound; it is a short, central Polish vowel
• final ę in muszę is often pronounced less strongly nasal than learners expect, especially in normal speech

Stress is usually on the next-to-last syllable in Polish, so:

• MU-szę
• PRZY-znać
• SER-nik
• PYSZ-ny

That regular stress pattern is very helpful when learning Polish pronunciation.