Ósmego czerwca nasza organizacja planuje wykład o zdrowiu, na który chcę pójść.

In Polish, when you say a date answering when?, you normally use:

• the day as an ordinal number
• the month in the genitive case

So:

• ósmy = eighth
• ósmego czerwca = on the eighth of June

The form ósmego is genitive, and czerwca is also genitive.

A useful pattern is:

• pierwszego stycznia = on the first of January
• drugiego maja = on the second of May
• ósmego czerwca = on the eighth of June

Also, month names in Polish are normally not capitalized, but Ósmego is capitalized here because it starts the sentence.

Because organizacja is a feminine singular noun, and the possessive adjective nasz must agree with it in:

• gender
• number
• case

So:

• nasz = masculine
• nasza = feminine
• nasze = neuter

Since organizacja is feminine, you get nasza organizacja.

It is in the nominative case, because it is the subject of the sentence:

nasza organizacja planuje... = our organization is planning...

The subject of a Polish sentence is usually in the nominative.

The verb planować usually takes a direct object, and that object goes into the accusative case.

Here, wykład is the object of planuje.

But wykład is a masculine inanimate noun, and in the singular, masculine inanimate nouns often have the same form in the nominative and accusative. So:

• nominative: wykład
• accusative: wykład

That is why the form does not change.

Because the preposition o meaning about/on the subject of takes the locative case.

So:

• zdrowie = health
• locative: zdrowiu

That gives:

• wykład o zdrowiu = a lecture about health

This is a very common pattern:

• książka o historii = a book about history
• rozmowa o pracy = a conversation about work
• wykład o zdrowiu = a lecture about health

Because na który chcę pójść is a relative clause describing wykład.

In Polish, relative clauses introduced by words like który, która, które are normally separated by a comma:

• To jest książka, którą czytam.
• To jest wykład, na który chcę pójść.

So the comma is standard Polish punctuation here.

Because the relative pronoun must match the construction required by the verb inside the relative clause.

Here the clause is:

• chcę pójść na wykład = I want to go to the lecture

The verb phrase is pójść na + accusative.

So when wykład is replaced by a relative pronoun, you keep na:

• na który chcę pójść = which I want to go to

Without na, the grammar would be wrong because pójść here needs na.

Because wykład is masculine singular inanimate, and the pronoun który has to agree with it in gender and number. Its case is accusative because of na.

For masculine singular nouns in the accusative:

• animate often takes którego
• inanimate takes który

Since wykład is inanimate, the correct form is:

• na który

Compare:

• mężczyzna, którego widzę = the man whom I see
• film, który oglądam = the film that I am watching
• wykład, na który chcę pójść = the lecture I want to go to

Because pójść is the more natural choice for a single, completed trip or visit, especially one in the future.

Here the speaker wants to attend one specific lecture, so chcę pójść fits well.

Very roughly:

• iść = to be going / to go (imperfective)
• pójść = to go, set off, go once (perfective)

So:

• chcę pójść na wykład = I want to go to the lecture

In this context, pójść sounds more natural than iść.

No, Polish word order is fairly flexible, but this version sounds natural and neutral.

Starting with Ósmego czerwca puts the date first, which is a common way to set the scene:

• Ósmego czerwca nasza organizacja planuje wykład o zdrowiu, na który chcę pójść.

You could also say something like:

• Nasza organizacja planuje ósmego czerwca wykład o zdrowiu, na który chcę pójść.

That is still correct, but the emphasis is slightly different. The original sentence foregrounds the date first.