Mi volas pasigi la semajnfinon ĉe la maro.

Yes. In this sentence, pasigi means to spend (time).

A useful comparison is:

• pasi = to pass, to go by
• pasigi = to cause to pass, so with time it becomes to spend

So:

• La semajnfino pasas. = The weekend passes.
• Mi pasigas la semajnfinon... = I spend the weekend...

This is the normal Esperanto verb for spending time. It is much better here than trying to use the English-style idea of spend directly.

Because Esperanto infinitives do not use a separate word like English to.

The infinitive is shown by the ending -i:

• voli = to want
• pasigi = to spend
• iri = to go

So in Mi volas pasigi..., the word pasigi already means to spend. No extra word is needed.

Because volas is the finite verb in the sentence: want / wants / am wanting in the present tense.

Esperanto verb endings are very regular:

• -i = infinitive, to want → voli
• -as = present tense → volas
• -is = past tense → volis
• -os = future tense → volos

So:

• Mi volas = I want
• Mi volis = I wanted
• Mi volos = I will want

Because it is the direct object of pasigi.

The speaker is spending what?
Answer: la semajnfinon

In Esperanto, direct objects usually take -n:

• Mi vidas la domon. = I see the house.
• Mi legas la libron. = I read the book.
• Mi volas pasigi la semajnfinon. = I want to spend the weekend.

So semajnfino becomes semajnfinon because it is the thing being spent.

Yes. It is a compound:

• semajno = week
• fino = end

So semajnfino literally means week-end.

This is very typical Esperanto word-building. Once you know the parts, many words become easy to understand.

Because pasigi is the normal Esperanto verb for spending time.

A very important beginner point:

• pasigi tempon / tagon / semajnfinon = to spend time / a day / a weekend
• spendi monon = to spend money

So Esperanto usually separates these two meanings more clearly than English does.

Natural:

• Mi pasigis du horojn tie. = I spent two hours there.
• Mi spendis multe da mono. = I spent a lot of money.

Here ĉe means something like at, by, or near.

So ĉe la maro means:

• at the sea
• by the sea
• at the seaside

It suggests location near the sea, not inside it.

This is a very common use of ĉe for being at or near a place.

Because en la maro means in the sea, literally inside the water.

Compare:

• ĉe la maro = by the sea / at the seaside
• en la maro = in the sea
• al la maro = to the sea (toward it)

So if you mean staying near the coast for the weekend, ĉe la maro is the right choice.

Because ĉe la maro is the natural way to say by the sea / at the seaside.

In Esperanto, la is often used when the noun refers to a clearly understood thing in the situation, or in a familiar location phrase like this one. The idea is not near some sea somewhere, but at the sea / seaside as a known kind of place.

So:

• ĉe la maro sounds natural
• ĉe maro would sound unusual or incomplete in most contexts

Because it is not the direct object.

In ĉe la maro, the noun is part of a prepositional phrase introduced by ĉe. Normally, nouns after prepositions do not take -n unless there is a special idea of direction.

Here there is no motion toward the sea; it is just location.

So:

• la semajnfinon gets -n because it is the direct object
• la maro does not get -n because it follows ĉe and simply shows location

The given order is the most neutral and natural:

• Mi volas pasigi la semajnfinon ĉe la maro.

But Esperanto word order is fairly flexible because endings show the grammar clearly.

You could move parts around for emphasis, for example:

• Ĉe la maro mi volas pasigi la semajnfinon.
  Emphasis on by the sea

• La semajnfinon mi volas pasigi ĉe la maro.
  Emphasis on the weekend

Still, for a learner, the original version is the best default pattern to copy.