Al mi mankas tempo por ripozi.

Because manki is commonly used like to be lacking to someone. In this pattern, the person who experiences the lack is marked with al.

So:

• Al mi mankas tempo = Time is lacking to me
• Natural English meaning: I lack time / I don't have time

A native English speaker often expects mi to be the subject, but here mi is not the subject. It is part of al mi, which shows the person affected.

The grammatical subject is tempo.

In Al mi mankas tempo por ripozi:

• tempo = the thing that is missing
• al mi = to me / for me
• mankas = is lacking
• por ripozi = to rest

So literally, the structure is closer to:

To me is lacking time to rest.

Even though that sounds unusual in English, it is normal in Esperanto.

Mankas is the present-tense form of manki, which means to be lacking, to be missing, or to be absent.

In this sentence, it does not mean that I am missing in the sense of being absent somewhere. It means that time is lacking to me.

Compare:

• Al mi mankas mono. = I lack money.
• Al ŝi mankas pacienco. = She lacks patience.

So manki often expresses that some thing is insufficient or unavailable for someone.

Because tempo is the subject, not the direct object.

The accusative -n is used for direct objects, but here tempo is the thing doing the grammatical role of subject with mankas.

So:

• tempo = subject
• al mi = indirect object / recipient-like phrase

That is why it is tempo, not tempon.

Por means for or in order to, and ripozi is the infinitive to rest.

So tempo por ripozi means:

• time to rest
• literally, time for resting / in order to rest

This is a very common Esperanto pattern:

• mono por vojaĝi = money to travel
• loko por sidi = a place to sit
• ŝanco por lerni = a chance to learn

Yes. That is a very natural alternative.

• Al mi mankas tempo por ripozi.
• Mi ne havas tempon por ripozi.

Both can mean I don't have time to rest.

The difference is mainly one of style and emphasis:

• Mi ne havas tempon... = straightforward, very easy for English speakers
• Al mi mankas tempo... = emphasizes the lack itself; slightly more literary or expressive in some contexts

Both are correct Esperanto.

Yes. Esperanto word order is fairly flexible.

You could also say:

• Mankas al mi tempo por ripozi.
• Tempo por ripozi mankas al mi.

These all mean roughly the same thing, but the emphasis changes:

• Al mi mankas tempo... puts early focus on to me
• Mankas al mi tempo... sounds a bit more neutral or stylistic
• Tempo por ripozi mankas al mi. emphasizes time to rest

The original sentence is perfectly normal.

Grammatically, al mi literally means to me, but in English the most natural translation is often I or for me.

With manki, it is often best to think:

• Al mi mankas X = I lack X
• or more literally, X is lacking to me

So yes, al is still the normal preposition to, but the whole expression works differently from English.

Yes, it is common and standard.

Esperanto often uses manki in this pattern:

• Al mi mankas tempo.
• Al li mankas mono.
• Al ni mankas sperto.

This is a very useful structure to learn because it appears often in both speech and writing.

It can be correct, but adding la changes the nuance.

• tempo = time in general
• la tempo = a specific, known time

So:

• Al mi mankas tempo por ripozi. = I lack time to rest.
• La tempo mankas al mi. = The time is lacking to me / I don't have the specific time.

In most general statements like this, tempo without la is the usual choice.

Yes. Besides al iu mankas io, you may also see related uses.

For example:

• Unu paĝo mankas en la libro. = One page is missing in the book.
• Li mankis en la kunveno. = He was absent from the meeting.
  (This is less directly related to the structure in your sentence, but it shows another use.)

Still, for learners, the most important pattern here is:

• Al + persono + mankas + thing

That pattern is the one used in Al mi mankas tempo por ripozi.

A very literal breakdown is:

• Al mi = to me
• mankas = is lacking
• tempo = time
• por ripozi = to rest

So the whole sentence is:

To me is lacking time to rest.

That is not natural English, but it helps show how Esperanto is building the idea. From there, the natural English meaning is simply:

I lack time to rest or I don't have time to rest.