Na stromě je zelený list.

Because na takes different cases depending on the meaning:

• na + locative = location, on / at
• na + accusative = movement onto something

Here the leaf is already located on the tree, so Czech uses the locative: na stromě.

Compare:

• List je na stromě. = The leaf is on the tree.
• Leze na strom. = He/she is climbing onto the tree.

Czech nouns change their endings according to case. The basic dictionary form is strom. After na in a location meaning, it has to be in the locative singular, which here is stromě.

So:

• strom = tree (basic form)
• na stromě = on the tree

This is just normal Czech declension.

Because list is the subject of the sentence, and subjects are normally in the nominative.

Czech word order is flexible, so the subject does not have to come first. Even though list comes after je, it is still the thing that is there, so it stays nominative:

• list = nominative singular

In English, word order shows the subject more strongly. In Czech, case endings do more of that work.

Because Czech adjectives must agree with the noun they describe in:

• gender
• number
• case

Here list is:

• masculine inanimate
• singular
• nominative

So the adjective must match that, giving zelený.

Examples of different agreement:

• zelený list = a green leaf
• zelená větev = a green branch
• zelené listy = green leaves

Czech does not have articles like English a/an and the.

So Na stromě je zelený list can mean something like:

• There is a green leaf on the tree
• A green leaf is on the tree

In another context, it might even be understood as the green leaf, but Czech usually leaves that to context rather than using an article.

Yes, both are possible, but they sound a little different.

• Na stromě je zelený list.
  This sounds like you are introducing what is located there: On the tree, there is a green leaf.

• Zelený list je na stromě.
  This sounds more like you are talking about the leaf and saying where it is: The green leaf is on the tree.

So the original sentence is very natural if the place na stromě is the starting point of the message.

Yes. In Czech, na stromě is the normal expression for something being on a tree or up in a tree.

So Czech commonly says:

• Pták je na stromě. = The bird is in the tree / on the tree.
• List je na stromě. = The leaf is on the tree.

English often uses in for something among the branches, but Czech usually uses na in these cases.

A simple learner-friendly approximation is:

• je ≈ ye
• stromě ≈ stro-mnye (roughly)

The letter ě usually affects the consonant before it and makes it sound softer. You do not pronounce it like a plain English e after a fully hard m.

So:

• Na stromě je... sounds roughly like na stro-mnye ye...

No. List can have several meanings, including:

• leaf
• sheet
• sometimes letter

But in Na stromě je zelený list, the meaning is clearly leaf, because of the context on the tree.

Je is the 3rd person singular form of být (to be), because list is singular: one leaf.

If you make the noun plural, the verb changes too:

• Na stromě je zelený list. = There is a green leaf on the tree.
• Na stromě jsou zelené listy. = There are green leaves on the tree.

So:

• je = is
• jsou = are