Tantus clamor in via est ut infans dormire non possit.

This is a result clause construction.

Latin often uses:

• a word showing degree in the main clause, such as tam, ita, sic, adeo, or tantus
• followed by ut
  • subjunctive
• to show the result or consequence

So tantus clamor ... ut ... means there is such a great noise ... that ...

Here:

• tantus = so great / such great
• ut infans dormire non possit = the result of that noise

The big clue is tantus.

A purpose clause usually tells you why someone does something. A result clause tells you what happens as a consequence.

Because the main clause already contains a word of degree, tantus, Latin is signaling:

• so great ... that ...

That makes ut infans dormire non possit a result clause, not a purpose clause.

Because possit is inside the ut result clause.

In Latin, result clauses regularly use:

• ut
• plus a subjunctive verb

So:

• main clause: Tantus clamor in via est
• result clause: ut infans dormire non possit

If you used potest, that would be indicative, and it would not match the normal grammar of a result clause.

Because the main verb is est, which is present tense.

Latin normally follows sequence of tenses:

• after a primary tense such as est, you usually get a present or perfect subjunctive
• after a secondary tense such as erat, you usually get an imperfect or pluperfect subjunctive

So:

• est ... ut ... possit = present main verb + present subjunctive
• if the sentence were in past time, you might expect erat ... ut ... posset

Because possum is normally followed by a complementary infinitive.

Latin says:

• possum dormire = I am able to sleep
• non possit dormire = he/she cannot sleep

So dormire is not a separate finite verb. It completes the meaning of possit.

Because it agrees with clamor.

Clamor is:

• masculine
• singular
• nominative

So the adjective describing it must match:

• tantus clamor

This is basic adjective agreement in Latin: adjectives agree with the nouns they modify in gender, number, and case.

Via is ablative singular.

That is because in with the ablative usually shows location:

• in via = in/on the street

A useful contrast:

• in via = location, in the street
• in viam = motion into, into the street

So here in via tells you where the noise is.

Infans is nominative singular, and it is the subject of possit.

So in the result clause:

• infans = the one who cannot sleep
• possit = the verb
• dormire = the infinitive depending on possit

Even though clamor is the subject of est in the main clause, the ut clause has its own subject, which is infans.

Because non is negating the verb possit.

The idea is:

• the baby is not able to sleep

In Latin, non often stands directly before the word it most clearly negates, or at least close to it. Here it naturally goes with possit.

So:

• dormire non possit = cannot sleep

Yes. Latin word order is much more flexible than English word order.

This sentence is arranged in a very natural and clear way:

• Tantus clamor first, to emphasize the cause
• in via next, to locate it
• est finishes the main clause
• ut infans dormire non possit gives the result

But Latin could rearrange parts for emphasis without changing the basic grammar, as long as the endings still make the relationships clear.