kahun ga ooi hi ha, me ga kayui node megusuri ga hituyou desu.

This is a very common Japanese pattern: a full clause comes before a noun and modifies it.

• 花粉が多い = there is a lot of pollen
• 日 = day

So:

• 花粉が多い日 = a day when there is a lot of pollen

Japanese does not need a word like when here. The modifying information simply goes before the noun.

In 花粉が多い, the が marks the thing that is abundant.

• 花粉 = pollen
• 多い = many / a lot / abundant

So 花粉が多い literally means something like pollen is abundant or there is a lot of pollen.

This is natural because 多い often works with が.

Yes. 花粉の多い日 is also very natural.

Both are used, and the difference is small in many situations:

• 花粉が多い日 feels like a clause: a day when pollen is abundant
• 花粉の多い日 feels a bit more like a fixed noun modifier: a high-pollen day

For a learner, it is good to recognize both.

The は makes days with a lot of pollen the topic.

So the sentence structure is roughly:

• As for days when there is a lot of pollen, ...

That is why the rest of the sentence talks about what is true on those days:

• 目がかゆいので目薬が必要です
• my eyes itch, so eyedrops are necessary

Because かゆい is an adjective, not a verb.

With adjectives that describe body conditions, Japanese often marks the body part with が:

• 目がかゆい = the eyes are itchy
• 頭が痛い = the head hurts / I have a headache
• のどが痛い = the throat hurts

Using を would not be correct with かゆい in this structure.

It can mean either in theory, because Japanese nouns do not have to show singular vs. plural. But in this sentence, it usually means the eyes in a general sense.

So 目がかゆい is naturally understood as my eyes itch or the eyes get itchy.

ので gives a reason, like because or so.

• 目がかゆいので、目薬が必要です
• Because my eyes are itchy, I need eyedrops

Compared with から, ので often sounds a bit softer, calmer, or more explanatory.

• ので = more neutral/explanatory
• から = often a bit more direct

Both can work here, but ので fits well in polite, matter-of-fact statements.

Because 必要 does not work like a normal verb that takes を.

必要 is a na-adjective (and also noun-like in some uses) meaning necessary. With 必要, the thing that is needed is often marked by が.

• 目薬が必要です = eyedrops are necessary / I need eyedrops

So this is a standard pattern:

• お金が必要です = money is necessary / I need money
• 時間が必要です = time is necessary / I need time

必要 is a na-adjective.

That is why you can say:

• 必要です = is necessary
• 必要なもの = necessary things

In this sentence, 目薬が必要です means eyedrops are necessary.

Yes. Japanese often leaves out subjects when they are obvious from context.

In English, you might say:

• On days with a lot of pollen, my eyes itch, so I need eyedrops.

In Japanese, 私 is not necessary if the speaker is clearly talking about themselves, or if the statement is meant generally.

So the sentence can sound like either:

• a personal statement about the speaker
• a general statement about what happens on high-pollen days

Context decides.

Yes, that is a good close reading of the Japanese structure.

Piece by piece:

• 花粉が多い日 は = as for days when there is a lot of pollen
• 目がかゆい = the eyes are itchy
• ので = because / so
• 目薬が必要です = eyedrops are necessary

This kind of literal breakdown is useful because Japanese often expresses ideas in a more topic-based way than English does.