W niedzielę ta sama grupa gra w siatkówkę na tym samym boisku.

Because of case after the preposition and the meaning.

• Niedziela is feminine: nominative niedziela.
• With days of the week, w + accusative usually means “on (that day)” in a time sense.

So:

• nominative: niedziela – Sunday (as a subject: Niedziela jest…)
• accusative: niedzielę – on Sunday (time expression: w niedzielę)
• locative: niedzieli – used after some prepositions for location, not time.

In time expressions you say:

• w niedzielę – on Sunday
• w sobotę, w środę, w sobotę wieczorem, etc.

So w niedzielę is the standard way to say on Sunday in this habitual/time sense.

Polish word order is flexible, and elements can be moved for emphasis or to set the scene.

• W niedzielę ta sama grupa gra…
  → Puts emphasis on when this happens; “As for Sunday / On Sunday, this same group plays…”.

You could also say:

• Ta sama grupa w niedzielę gra w siatkówkę na tym samym boisku.
• Ta sama grupa gra w siatkówkę w niedzielę na tym samym boisku.

All are grammatically correct. The basic information doesn’t change; only the focus / rhythm does. Starting with the time expression is very common in Polish.

Because of grammatical gender and agreement.

• Grupa is grammatically feminine (ends in -a and declines like typical feminine nouns).
• The demonstrative ten/ta/to must match the noun’s gender:
  • masculine: ten
  • feminine: ta
  • neuter: to

The phrase “the same” is expressed as ten sam / ta sama / to samo, again agreeing with the noun:

• masculine: ten sam chłopak – the same boy
• feminine: ta sama dziewczyna – the same girl
• feminine: ta sama grupa – the same group
• neuter: to samo miejsce – the same place

So with grupa (feminine), the correct form is ta sama grupa.

Without sama, ta grupa just means “this group”.

With sama, ta sama grupa means “the same group (as before / as previously mentioned)”.

Compare:

• Ta grupa gra w siatkówkę. – This group plays volleyball.
• Ta sama grupa gra w siatkówkę. – The same group plays volleyball. (the same one you already know about, for example the same group that did something on Saturday)

So sama here means “same” in the sense of identical, not a different one.

Because in Polish, grupa is grammatically singular, even though it refers to many people.

• grupa → 3rd person singular feminine noun
• The verb agrees with the noun’s grammatical number and person, not with the “real-world” number of people inside the group.

So:

• Ta grupa gra w siatkówkę. – This group plays volleyball. (verb: 3rd singular)
• Te grupy grają w siatkówkę. – These groups play volleyball. (now plural: grupy, so verb: grają)

It’s similar to saying in English “The team *is winning”* (not “are winning”) in standard American English: the noun is grammatically singular.

For sports and games, Polish usually uses the pattern:

• grać w + [sport/game in accusative]

So:

• grać w siatkówkę – to play volleyball
• grać w piłkę nożną – to play football / soccer
• grać w tenisa – to play tennis
• grać w szachy – to play chess

You can see grać siatkówkę in informal speech, but grać w siatkówkę is the standard, neutral form and the one you should learn first.

Because of the case required by the construction grać w + accusative.

• Base/nominative form: siatkówka (volleyball)
• Accusative singular (feminine): siatkówkę

So:

• Co oni robią? – Oni grają w siatkówkę.
  What are they doing? – They are playing volleyball.

The -ę ending is the normal accusative ending for many feminine nouns ending in -ka (e.g. koleżanka → koleżankę, piłka → piłkę).

Polish makes a distinction:

• grać w + accusative → to play (a game/sport)

  • grać w siatkówkę – to play volleyball
  • grać w piłkę – to play ball
  • grać w karty – to play cards

• grać na + locative → to play (a musical instrument)

  • grać na gitarze – to play the guitar
  • grać na pianinie – to play the piano
  • grać na skrzypcach – to play the violin

So gra w siatkówkę fits the “sport/game” pattern.

Because of the typical prepositions used with places and activities.

• boisko is a playing field / sports ground.
• For open areas like fields, courts, and pitches, Polish usually uses na:
  • na boisku – on/at the sports field
  • na stadionie – at the stadium
  • na placu – in the square / on the square
  • na lotnisku – at the airport

You’d normally only use w when you are inside something:

• w domu – in the house
• w budynku – in the building

Since you are on the pitch, not inside it, you say na boisku, and here specifically na tym samym boisku – on the same pitch/field.

It is locative singular, required by the preposition na when it means location.

• Preposition na:
  • na + accusative – movement onto: idę na boisko (I’m going to the field)
  • na + locative – location on: jestem na boisku (I am at/on the field)

Here we have location (the group is playing there), so na + locative:

• boisko (neuter, nominative)
• locative singular: (na) boisku

The adjectives and demonstrative also go into locative singular neuter:

• ten sam (nom.) → tym samym (loc.)
• boisko (nom.) → boisku (loc.)

So: na tym samym boisku = on the same field.

Ten sam / ta sama / to samo behaves like ten / ta / to plus an agreeing adjective sam/sama/samo.

Neuter singular (as with boisko) has:

• Nominative: to samo boisko
• Accusative: to samo boisko
• Locative: tym samym boisku
• Dative: temu samemu boisku

So in our sentence:

• neuter noun in locative: boisku
• demonstrative in neuter locative: tym
• adjective in neuter locative: samym

Together: na tym samym boisku.

Yes, that would still be correct, but the meaning would be slightly less specific.

• na tym boisku – on this field
• na tym samym boisku – on the same field (the same one as before; not another one)

So samym emphasizes that it is the same field as in some earlier context (e.g. the same field they used on Saturday).

Yes. Polish word order is quite flexible, especially for adverbials (time, place, manner). All of these are acceptable:

• W niedzielę ta sama grupa gra w siatkówkę na tym samym boisku.
• Ta sama grupa w niedzielę gra w siatkówkę na tym samym boisku.
• Ta sama grupa gra w siatkówkę w niedzielę na tym samym boisku.
• Ta sama grupa gra w siatkówkę na tym samym boisku w niedzielę.

The core structure is: [subject] gra [w siatkówkę] [adverbials…]. Moving the time/place phrases changes focus and rhythm, not basic meaning.

Polish, like English, can use the present tense for habitual/repeated actions:

• Ta sama grupa gra w siatkówkę w niedzielę.
  → This same group plays volleyball on Sunday (every Sunday / on Sundays).

There’s no need to add anything like “usually” in Polish; the combination of present tense + a time expression (w niedzielę) is enough to show it’s a regular activity (unless context says it’s just this one Sunday).