Uti wa mti huu ni mnene.

A helpful way to break it up is:

• uti = the trunk/stem/core/inside wood part (depending on context and dictionary choice)
• wa mti huu = of this tree
• ni mnene = is thick

So the sentence is structured like:

[subject noun] + [of-phrase] + [copula] + [adjective]

More literally:

Uti wa mti huu = the trunk/stem of this tree
ni mnene = is thick

The whole subject is uti wa mti huu, not just uti by itself.

Wa is the connector used here to mean of.

In Swahili, possession or association is often made with a linking word that agrees with the first noun, not with English-style word order. So:

• uti wa mti = the trunk/stem of a tree
• uti wa mti huu = the trunk/stem of this tree

A native English speaker often expects something more like tree’s trunk, but Swahili usually does it as:

thing possessed + connector + possessor

So:

• uti = the thing being talked about
• wa mti huu = belonging to / associated with this tree

In Swahili, demonstratives such as this usually come after the noun.

So:

• mti huu = this tree
• not huu mti

This is very normal Swahili word order. English puts this before the noun, but Swahili usually puts the demonstrative after it.

That means in this sentence:

• mti huu = this tree

It describes mti, because it comes right after mti.

So:

• uti wa mti huu = the trunk/stem of this tree

It does not mean this trunk/stem of the tree.

If you wanted this trunk/stem of the tree, you would move the demonstrative so it follows uti instead:

• uti huu wa mti

So position matters a lot. In your sentence, huu clearly goes with mti.

Yes. Ni is functioning like is here.

It links the subject to a description:

• Uti wa mti huu = subject
• ni = is
• mnene = thick

So ni is the copula, the word that connects X with Y in sentences like:

• A is B
• The tree trunk is thick

In beginner terms, it is perfectly fine to think of ni here as is.

Because adjectives in Swahili usually agree with the noun class of the noun they describe.

The noun being described is uti, so the adjective takes the matching form:

• base idea: -nene = thick/fat
• matching form here: mnene

This is part of Swahili noun-class agreement, which affects things like:

• adjectives
• demonstratives
• possessive connectors
• verbs in many cases

So mnene is not random; it is the form that agrees with the noun being described.

Because these nouns belong to noun classes that use similar agreement patterns in the singular.

That is why you see forms like:

• wa
• huu
• mnene

A learner may expect each noun to behave very differently, but in this case the patterns happen to look similar. That can be confusing at first, because it makes it look as if everything is using the same form for the same reason. In reality, each agreeing word is matching the noun it belongs to:

• wa matches uti
• huu matches mti
• mnene matches uti

So the same-looking pattern can appear more than once in one sentence.

There is no separate word for the or a here, because Swahili normally does not use articles the way English does.

Whether something is understood as:

• a tree
• the tree
• this tree

depends on context and on words like demonstratives.

In this sentence, huu makes mti specific:

• mti huu = this tree

So Swahili often leaves article meanings to context rather than using separate words like English does.

Yes, but it would mean something different.

• Mti huu ni mnene = This tree is thick
• Uti wa mti huu ni mnene = The trunk/stem/core of this tree is thick

So your original sentence focuses on a part of the tree, not the whole tree.

That is an important distinction. Swahili is being very precise here: it is not necessarily saying the whole tree is thick, only that the uti is.