По сравнению с прошлым чемпионатом наша команда играет увереннее.

Yes. По сравнению с is a very common fixed expression meaning in comparison with or compared with.

A useful pattern is:

по сравнению с + instrumental case

So in this sentence, по сравнению с прошлым чемпионатом means compared with the previous championship.

You should learn по сравнению с as a whole chunk, because Russian often expresses comparison this way instead of using a direct than structure.

Because the preposition с in the expression по сравнению с requires the instrumental case.

So:

• прошлый чемпионат = nominative
• с прошлым чемпионатом = instrumental after с

Both words change because the adjective must agree with the noun:

• прошлый → прошлым
• чемпионат → чемпионатом

This is a very normal agreement pattern in Russian.

Because команда is grammatically singular in Russian.

Even though a team is made up of many people, the noun команда is a singular feminine noun, so the verb is also singular:

• команда играет
• not команда играют

This works much like English the team is playing... in standard singular agreement.

Because команда is a feminine noun.

The possessive pronoun наш has to agree with the noun in gender, number, and case:

• masculine: наш
• feminine: наша
• neuter: наше
• plural: наши

So:

• наш стол
• наша команда
• наше место
• наши друзья

Here it functions as an adverbial comparative, because it describes how the team plays.

• играть уверенно = to play confidently
• играть увереннее = to play more confidently

Even though the form looks similar to an adjective comparative, in this sentence it modifies the verb играет, so in English it corresponds to more confidently, not more confident.

It is the comparative form built from уверенный / уверенно.

A very common Russian comparative pattern is:

• -ее / -ей
• sometimes with small stem changes

Here:

• уверенно = confidently
• увереннее = more confidently

You will see similar forms such as:

• быстро → быстрее
• медленно → медленнее
• громко → громче

So увереннее is a normal comparative form meaning more confidently.

Yes, absolutely.

Both are possible:

• играет увереннее
• играет более уверенно

The form with увереннее is a simple synthetic comparative and often sounds a bit more natural and compact in everyday Russian. Более уверенно is also correct, just slightly more analytical in style.

Because Russian is expressing the comparison with the phrase по сравнению с..., not with чем.

In English, you might think of:

• more confidently than before
• more confidently than in the previous championship

Russian often avoids a direct than and instead says:

• по сравнению с прошлым чемпионатом

So the sentence structure is more like:

In comparison with the previous championship, our team plays more confidently.

A version with чем is also possible in some contexts, but this sentence uses a different comparison structure.

Russian present tense often covers both English simple present and present continuous, depending on context.

So играет can mean:

• plays
• is playing

In this sentence, the idea is probably something like the team is playing more confidently now / these days / in the current championship, compared with the previous one.

Russian does not need a separate continuous form like English does.

No, Russian word order is fairly flexible.

This version:

По сравнению с прошлым чемпионатом наша команда играет увереннее.

puts the comparison first, which sets the frame right away: compared with the previous championship...

You could also say:

Наша команда по сравнению с прошлым чемпионатом играет увереннее.

That is also natural. The original word order is just a very normal way to highlight the comparison at the beginning.

Чемпионат usually means championship, tournament, or sometimes league competition / season, depending on context.

So прошлый чемпионат means the previous championship or the last tournament/competition. The exact English wording depends on what sport or competition the sentence is talking about.

A helpful stress guide is:

По сравнЕнию с прОшлым чемпионАтом нАша комАнда игрАет уверенЕе.

A few notes:

• сравнЕнию: stress on Е
• прОшлым: stress on О
• чемпионАтом: stress on А
• нАша
• комАнда
• игрАет
• уверенЕе: stress on the last Е

If you say it smoothly, по сравнению с often sounds like one connected chunk, which is another good reason to memorize it as a set expression.