По сравнению с первым таймом второй был спокойнее.

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

In this sentence, it sets up the standard of comparison:

По сравнению с первым таймом = Compared with the first half

So the whole sentence literally works like:

Compared with the first half, the second was calmer.

Because по сравнению с requires the instrumental case.

So:

• первый тайм = nominative
• с первым таймом = instrumental after с in this expression

Both words change:

• первый → первым
• тайм → таймом

This is one of the main things to remember with по сравнению с: it is followed by the instrumental.

Тайм is a sports word meaning half or sometimes period, depending on the sport.

In this sentence:

• первый тайм = the first half
• второй тайм = the second half

A native English speaker will most often understand it as the two halves of a match, especially in football/soccer.

Because Russian often leaves out a noun when it is obvious from context.

Here, второй really means второй тайм. The noun тайм is omitted because it has already been established by первым таймом.

So:

• full version: По сравнению с первым таймом второй тайм был спокойнее.
• natural shorter version: По сравнению с первым таймом второй был спокойнее.

English can do something similar:

• The first half was intense; the second was calmer.

Because the omitted noun is тайм, and тайм is masculine.

Even when the noun is left out, the adjective and past-tense verb still agree with it:

• второй because тайм is masculine
• был because the subject is understood as второй тайм, masculine singular

If the hidden noun were feminine, the forms would be different.

Спокойнее is the comparative form of спокойный / спокойно.

It means calmer, quieter, more спокойный/спокойно.

A very important point: Russian simple comparatives like спокойнее, лучше, интереснее usually do not change for gender, number, or case.

So you do not make it agree with the noun. You just use the same form:

• тайм был спокойнее
• игра была спокойнее
• матчи были спокойнее

The comparative stays спокойнее in all these examples.

It depends on context, but in a sports sentence it usually means something like:

• calmer
• less tense
• less hectic
• less eventful
• more controlled

So it does not necessarily mean literally quieter in the sense of sound. It often describes the overall pace or intensity of the half.

Yes. That is also correct.

Russian has more than one way to express comparison:

1. По сравнению с первым таймом второй был спокойнее.

   • more explicit: compared with the first half

2. Второй тайм был спокойнее первого тайма.

   • a direct comparison using the comparative + genitive

Very often Russian shortens the second version too:

• Второй тайм был спокойнее первого.

That is natural because тайм is understood.

So the sentence you were given is not the only possible way to say this idea; it is just one very common and clear way.

Yes, the word order can be changed.

The given sentence starts with the comparison phrase:

По сравнению с первым таймом второй был спокойнее.

This puts the comparison frame first: compared to the first half...

You could also say:

• Второй тайм был спокойнее по сравнению с первым.
• Второй был спокойнее по сравнению с первым таймом.

These are understandable too. Russian word order is flexible, and changes mostly affect emphasis and style rather than basic meaning.

The original version sounds natural because it introduces the reference point first and then gives the main statement.

Because по сравнению с первым таймом is functioning as a normal adverbial phrase, not as a parenthetical insert.

So the neutral punctuation is:

По сравнению с первым таймом второй был спокойнее.

A comma is sometimes seen in longer or more stylistically marked sentences, but in a plain sentence like this, no comma is the standard choice.