Ja sam muszę podpisać ten dokument.

Yes — muszę already tells you the subject is I, so ja is not grammatically necessary.

Polish often drops subject pronouns when the verb ending makes the subject clear. So:

• Muszę podpisać ten dokument. = I have to sign this document.

Adding ja gives extra emphasis or contrast, for example:

• Ja muszę podpisać ten dokument, nie ty.
  I have to sign this document, not you.

So in Ja sam muszę podpisać ten dokument, ja helps stress that it is specifically me.

Here sam means something like:

• myself
• alone
• personally

So Ja sam muszę podpisać ten dokument means that I myself have to sign it, or I have to sign it personally.

It adds the idea that no one else can do it for me.

Compare:

• Muszę podpisać ten dokument. = I have to sign this document.
• Ja sam muszę podpisać ten dokument. = I myself have to sign this document.

Because sam has to match the person it refers to.

In this sentence it refers to ja and is in the nominative singular masculine form:

• sam = masculine
• sama = feminine
• samo = neuter

So:

• said by a man: Ja sam muszę podpisać ten dokument.
• said by a woman: Ja sama muszę podpisać ten dokument.

Forms like samego are used in different grammatical contexts, not here.

Only sam changes:

• Ja sama muszę podpisać ten dokument.

Everything else stays the same.

That is because sam/sama agrees with the speaker’s gender.

Muszę is the 1st person singular present tense of musieć (to have to / must).

So:

• muszę = I must / I have to
• musisz = you must
• musi = he/she/it must

Even though it is present tense in form, it often translates naturally into English as I have to.

Because after musieć (must / have to), Polish normally uses an infinitive.

So the structure is:

• muszę podpisać = I must sign

Other examples:

• Muszę iść. = I have to go.
• Muszę zadzwonić. = I have to call.

This is very similar to English must + verb.

This is a question of aspect, which is very important in Polish.

• podpisać = perfective → to sign, as a completed action
• podpisywać = imperfective → to be signing / to sign repeatedly / to sign in a general sense

In this sentence, the speaker means one complete act of signing a specific document, so podpisać is the natural choice:

• Muszę podpisać ten dokument. = I have to sign this document.

If you used podpisywać, it would sound less natural here unless the context focused on repetition, process, or habit.

Because dokument is the direct object of podpisać, so it is in the accusative case.

For a masculine inanimate noun like dokument, the accusative singular looks the same as the nominative:

• nominative: ten dokument
• accusative: ten dokument

So although the form does not change, the case is still accusative.

By contrast, some masculine animate nouns do change in the accusative.

Yes. Polish word order is flexible, and changing it usually changes the emphasis, not the basic meaning.

For example:

• Ja sam muszę podpisać ten dokument.
  Emphasis on I myself.
• Muszę sam podpisać ten dokument.
  Emphasis on the fact that I must do it personally.
• Ten dokument muszę sam podpisać.
  Emphasis on this document.

The sentence you were given sounds natural and strongly highlights the speaker.

Not exactly.

• sam in this sentence means myself / personally / alone
• samotnie means more literally alone / solitarily, often describing being by oneself
• samemu can also mean by oneself, but in a different structure

Examples:

• Zrobię to sam. = I’ll do it myself.
• Mieszkam samotnie. = I live alone.
• Muszę to zrobić samemu. = I have to do it by myself.

In your sentence, sam is the most natural choice.

No, it is neutral and natural. It can be used in everyday speech as well as in more formal situations, especially because dokument is a formal-type noun.

Depending on tone and context, it can sound:

• neutral: I myself have to sign this document.
• emphatic: No, I personally have to sign it.
• slightly frustrated: I have to sign this document myself.

So the grammar is neutral; the situation decides the tone.

Polish stress is usually on the second-to-last syllable.

podpisać is pronounced roughly like:

• pod-PI-sać

The stress is on PI.

A rough English-style approximation could be:

• pod-PEE-sach

But the final ć is a soft sound, so that English approximation is only approximate.

Yes, depending on context.

Ja sam muszę podpisać ten dokument can suggest:

1. I personally must sign it
   nobody can sign in my place

or

2. I alone have to sign it
   I am the only one who has this obligation

Usually the surrounding context makes the intended meaning clear. The word sam often naturally covers both ideas of myself and alone.