Hra skončila remízou.

Yes. Hra means game.

It is the subject of the sentence, so Hra skončila remízou literally means something like The game ended in a draw or The game finished as a draw.

A useful related form is:

• hra = game
• hry = games / of the game, depending on context

Skončila means ended or finished.

Its base form is skončit, which means to end / to finish.

In this sentence, skončila is:

• past tense
• singular
• feminine

It is feminine because it agrees with hra, and hra is a feminine noun.

So:

• hra skončila = the game ended
• if the subject were masculine, the past form would look different
• if the subject were neuter, it would also look different

Because the subject hra is feminine singular, and Czech past tense agrees with the gender and number of the subject.

So with skončit in the past tense:

• masculine singular: skončil
• feminine singular: skončila
• neuter singular: skončilo
• plural forms differ too

Since hra is feminine, Czech uses skončila.

Because after skončit in this meaning, Czech often uses the instrumental case to express the result or outcome.

The basic noun is:

• remíza = draw, tie

But in the sentence it becomes:

• remízou = with a draw / as a draw / in a draw

So:

• Hra skončila remízou = The game ended in a draw

This is a very common Czech pattern:

• skončit vítězstvím = to end in victory
• skončit porážkou = to end in defeat
• skončit remízou = to end in a draw

Remízou is in the instrumental singular.

The noun remíza is a feminine noun, and its instrumental singular form is remízou.

So the case pattern here is:

• nominative: remíza
• instrumental: remízou

In this sentence, the instrumental shows the outcome of the game.

A Czech learner may wonder that because English says ended in a draw, but the natural Czech wording is skončila remízou.

Using v remíze here is not the standard way to say it. The idiomatic expression is with the instrumental:

• skončit remízou

So the sentence you should learn is:

• Hra skončila remízou.

This is one of those places where Czech structure does not match English word-for-word.

Yes, it matters.

Skončit is perfective. It refers to a completed action: the game reached its end.

That fits this sentence perfectly, because the game is over and we are talking about the completed result.

The imperfective partner is usually:

• končit = to be ending / to end in a more ongoing or repeated sense

Compare:

• Hra skončila remízou. = The game ended in a draw.
• Hra už končila. = The game was already coming to an end.

So in your sentence, perfective skončila is the natural choice.

Yes, Czech word order is flexible, but the neutral order here is:

• Hra skončila remízou.

Other orders are possible, but they change emphasis:

• Remízou skončila hra. = more marked, emphasizing the draw
• Skončila hra remízou. = possible in special contexts, but not the most neutral

For a learner, the standard version to use is:

• Hra skončila remízou.

Approximately:

• reh-MEE-zoh

A bit more exactly in Czech sounds:

• re as in a short reh
• mí has a long í, so hold the vowel a little: mee
• zou sounds roughly like zoh with a long ou diphthong

Also note:

• the stress in Czech is normally on the first syllable, so RE-mízou

Yes, broadly speaking.

Remíza is the Czech word for a game or match where neither side wins.

Depending on the variety of English and the sport, this may be translated as:

• draw
• tie

So:

• Hra skončila remízou. = The game ended in a draw.
• In some contexts, especially American English, someone might say The game ended in a tie.

A few very useful ones:

• Zápas skončil remízou. = The match ended in a draw.
• Turnaj skončil vítězstvím domácích. = The tournament ended with a victory for the home team.
• Sezóna skončila porážkou. = The season ended in defeat.
• Jednání skončilo dohodou. = The negotiations ended in an agreement.

These help you see the same pattern:

• skončit + instrumental = to end in / to end with / to end as something