Ni bezonas ne nur permeson, sed ankaŭ sponsoron.

It means not only ..., but also ....

So:

• ne nur permeson = not only permission
• sed ankaŭ sponsoron = but also a sponsor

This is a very common Esperanto pattern, and it works much like English:

• Ŝi estas ne nur inteligenta, sed ankaŭ afabla. = She is not only intelligent, but also kind.

The -n ending marks the direct object in Esperanto.

In this sentence, the thing we need is:

• permeson = permission
• sponsoron = a sponsor

Because they are both objects of bezonas (need), they take -n.

Compare:

• Ni bezonas permeson. = We need permission.
• La permeso estas ĉi tie. = The permission/permit is here.

In the second sentence, permeso is the subject, so there is no -n.

No. In Esperanto, verbs do not change according to the subject.

So:

• mi bezonas = I need
• vi bezonas = you need
• li bezonas = he needs
• ni bezonas = we need
• ili bezonas = they need

The ending -as always means present tense.

That makes Esperanto much simpler than English in this area.

The dictionary form is bezoni, which means to need.

Esperanto verb endings work like this:

• bezoni = to need
• bezonas = need / needs
• bezonis = needed
• bezonos = will need
• bezonu = need! / should need
• bezonus = would need

So Ni bezonas ... literally means We need ...

Esperanto has no indefinite article like English a/an.

It does have a definite article, la, meaning the, but you only use it when needed.

So:

• sponsoro can mean a sponsor or just sponsor
• la sponsoro means the sponsor

In your sentence, sponsoron is indefinite, so no article is necessary.

Likewise, permeson can be understood as permission or a permit/permission, depending on context.

Permeso means permission.

Depending on context, English might translate it as:

• permission
• authorization
• sometimes a permit, if the situation is concrete enough

The root is permes-, related to allowing or permitting.

Examples:

• Mi ne havas permeson. = I don’t have permission.
• Ili donis al ni permeson. = They gave us permission.

Yes, sponsoro is a normal Esperanto noun. It means sponsor.

Like many Esperanto nouns, it ends in -o:

• sponsoro = sponsor
• sponsoron = sponsor, as a direct object

Esperanto often uses internationally recognizable roots, especially for modern ideas. So a native English speaker will often notice familiar words like this.

Because sed ankaŭ is the natural way to say but also.

So the whole contrast pattern is:

• ne nur X, sed ankaŭ Y
• not only X, but also Y

That said, Esperanto word order is fairly flexible, but this is the standard and most natural arrangement here.

The basic meaning would still be understood in some other orders, because Esperanto uses endings like -n to show grammar. But Ni bezonas ne nur permeson, sed ankaŭ sponsoron is the most natural wording.

This pattern is best learned as a chunk:

• ne nur ..., sed ankaŭ ...

If you move the parts around too much, the sentence may sound awkward even if it is still understandable.

Because sed means but, and Esperanto normally uses a comma before it when it links two contrasting parts.

So:

• Ni bezonas ne nur permeson, sed ankaŭ sponsoron.

This punctuation is very standard.

Yes. Adjectives agree with the nouns they describe, including the -n ending.

For example:

• Ni bezonas specialan permeson. = We need a special permission/permit.
• Ni bezonas riĉan sponsoron. = We need a rich sponsor.

Here:

• speciala → specialan
• riĉa → riĉan

because they describe direct objects.

You would add -j for plural, and if the noun is also a direct object, it gets -jn.

Examples:

• Ni bezonas ne nur permesojn, sed ankaŭ sponsorojn. = We need not only permissions/permits, but also sponsors.

So the pattern is:

• singular object: -on
• plural object: -ojn

For adjectives, the same agreement applies:

• gravajn permesojn
• malavarajn sponsorojn