uekibati ni hatizokoana ga aru.

A natural reading is:

うえきばち に はちぞこあな が ある。

Breakdown:

• 植木鉢 = うえきばち
• 鉢底穴 = はちぞこあな
• ある = ある

In normal Japanese writing, spaces are usually not used, so you would normally see:

植木鉢に鉢底穴がある。

This sentence follows the very common pattern:

Place に Thing が ある

It means there is / exists a thing in a place.

So here:

• 植木鉢に = in the flowerpot / on the flowerpot
• 鉢底穴が = a drainage hole / a hole at the bottom of the pot
• ある = exists / there is

This pattern is one of the most important ways Japanese expresses existence for inanimate things.

に marks the location where something exists.

So in:

• 植木鉢に
  the に tells you that the flowerpot is the place where the hole exists.

This is different from English, where we often say in, on, or at. Japanese に is broader here and simply marks the location of existence.

A good way to remember it is:

• X に Y がある = There is Y in/at X

In this sentence, が marks the thing that exists: 鉢底穴.

So:

• 鉢底穴がある = there is a bottom hole / drainage hole

Using が is normal in existence sentences because it introduces or points out what is there.

Compare:

• 植木鉢に鉢底穴がある。
  = There is a drainage hole in the flowerpot.

• 鉢底穴はある。
  = As for the drainage hole, it exists. / There is a drainage hole, at least.
  This sounds more contrastive or topic-based.

So が is the most neutral choice here.

Japanese uses:

• ある for inanimate things
• いる for animate things such as people and animals

A hole is not animate, so ある is correct.

Examples:

• 机の上に本がある。 = There is a book on the desk.
• 庭に猫がいる。 = There is a cat in the yard.

Since 鉢底穴 is a thing, not a living being, you use ある.

Because it is a compound noun.

It is made from:

• 鉢 = pot
• 底 = bottom
• 穴 = hole

Together, they form one noun meaning something like pot-bottom hole or drainage hole at the bottom of a pot.

Japanese often combines nouns directly like this, without using words like of.

Compare:

• 日本語 = Japanese language
• 電車駅 would sound odd, but 地下鉄駅 = subway station
• 台所窓 could mean kitchen window in a compound style

So 鉢底穴 is functioning as a single noun.

It is understandable, but in real life Japanese may also use other expressions depending on context, such as:

• 底穴 = bottom hole
• 鉢底の穴 = the hole in the bottom of the pot

So 鉢底穴 is structurally natural as a compound, but in some contexts a speaker might choose a different phrasing that sounds a little more ordinary or easier to process.

For learning purposes, though, it is a good example of how Japanese packs information into noun compounds.

Japanese normally does not mark articles or plural the way English does.

So:

• 植木鉢 can mean a flowerpot, the flowerpot, or flowerpots, depending on context
• 鉢底穴 can mean a drainage hole, the drainage hole, etc.

The exact interpretation comes from the situation, not from separate words like a/the.

This is very common in Japanese, so learners need to get used to letting context do that job.

Yes, Japanese word order is somewhat flexible, as long as the particles stay correct.

For example, you could say:

• 植木鉢に鉢底穴がある。
  Neutral: There is a drainage hole in the flowerpot.

• 鉢底穴が植木鉢にある。
  Also grammatical, but it puts more focus on 鉢底穴 first.

That said, the original order is the most natural for a plain existence statement following the pattern Place に Thing が ある.

植木鉢は鉢底穴がある is not the best natural version.

If you want to make 植木鉢 the topic, a more natural sentence would be something like:

• 植木鉢には鉢底穴がある。

Here, には combines:

• は = topic/contrast
• に = location

This gives a nuance like:

• As for the flowerpot, it has a drainage hole
• or There is a drainage hole in the flowerpot

It can sound contrastive, as if talking about the flowerpot in particular.

The original 植木鉢に鉢底穴がある is more neutral and straightforward.

Literally, it is an existence sentence:

• In the flowerpot, a drainage hole exists.

But in English, we often translate that more naturally as a kind of possession:

• The flowerpot has a drainage hole.

Japanese often uses existence structures where English prefers have.

So this sentence is grammatically an existence sentence, even if the English meaning may sound possessive.