Ni metas manĝrestaĵojn en kompoŝton.

Because it is the direct object of metas and it is plural.

• -o = noun
• -j = plural
• -n = accusative/direct object

So:

• restaĵo = a leftover, a remnant
• restaĵojn = leftovers / scraps, as the thing being put somewhere

Since we put food scraps, those scraps are the direct object, so Esperanto uses -n.

This is a very common Esperanto pattern.

With en, you can have:

• en + nominative for location: in
• en + accusative (-n) for direction/movement into: into

So:

• en kompoŝto = in compost
• en kompoŝton = into compost

In this sentence, the scraps are being moved into the compost, so kompoŝton takes -n.

Not if you want the idea of putting something into the compost.

• Ni metas manĝrestaĵojn en kompoŝton. = We put food scraps into compost.
• ... en kompoŝto would sound more like the scraps are already located in compost, not moving into it.

So en kompoŝton is the natural choice here because metas implies movement to a destination.

It is a compound word:

• manĝ- = food / eating
• restaĵ- = remains, leftovers, residue
• -o = noun
• -j = plural
• -n = accusative

So manĝrestaĵoj means food leftovers / food scraps, and manĝrestaĵojn is that word in the plural accusative.

This kind of compounding is extremely common in Esperanto.

In Esperanto, verbs do not change according to the subject.

The ending -as always means present tense:

• mi metas = I put / am putting
• vi metas = you put
• ni metas = we put
• ili metas = they put

So metas stays the same no matter who is doing the action. The subject ni tells you it means we.

Yes, meti is the normal Esperanto verb for to put, place, set.

So Ni metas ... means We put ...

Depending on context, Esperanto could sometimes use a more specific verb, but meti is the basic and very natural choice here.

Esperanto does not require an article in many cases where English might use nothing or might use some.

• manĝrestaĵojn can simply mean food scraps
• kompoŝton can mean compost

Esperanto has la for the, but it is only used when the noun is definite in a clear way.

So you could say:

• Ni metas la manĝrestaĵojn en la kompoŝton. = We put the food scraps into the compost.

That would suggest specific scraps and specific compost. Without la, the sentence is more general.

Because Esperanto normally uses an explicit subject pronoun like English does.

• mi = I
• vi = you
• li/ŝi/ĝi = he/she/it
• ni = we
• ili = they

The verb ending shows the tense, not the person. So metas only tells you it is present tense; ni tells you who is doing it.

A quick guide:

• ĝ sounds like j in judge
• ŝ sounds like sh in shoe
• ĵ sounds like the s in measure or the g in beige

So roughly:

• manĝrestaĵojn ≈ mahnj-resta-zhoyn
• kompoŝton ≈ kom-posh-ton

Also, Esperanto stress is usually on the second-to-last syllable.

It combines two endings:

• -oj = plural noun ending, pronounced roughly like oy
• -n = accusative ending

So -ojn is pronounced roughly like oyn.

That is why manĝrestaĵojn ends with a sound something like -zhoyn.

Yes, you could.

Enmeti means to put in / insert, so it is more specific than meti.

• Ni metas manĝrestaĵojn en kompoŝton. = We put food scraps into compost.
• Ni enmetas manĝrestaĵojn en kompoŝton. = We put food scraps into compost / We place food scraps in there.

Both are understandable. The version with metas is simple and very natural.