Imperator certe scit pacem meliorem esse quam bellum.

Because this is an indirect statement (Latin accusative + infinitive) after scit (he knows). In an indirect statement, the “subject” of the infinitive is put in the accusative, not the nominative.
So pacem ... esse = (that) peace is ... with pacem as the accusative subject of esse.

It’s an indirect statement (oratio obliqua) using accusative + infinitive:

• main verb: scit (knows)
• accusative subject: pacem
• infinitive: esse
• predicate adjective: meliorem
• comparison: quam bellum

meliorem agrees with pacem in case, number, and gender:

• pacem = accusative singular feminine (from pax, pacis)
• therefore meliorem = accusative singular feminine (comparative of bonus)

In an indirect statement, predicate adjectives with esse typically agree with the accusative “subject” (pacem).

certe is an adverb meaning certainly / surely. Here it most naturally modifies scit:
Imperator certe scit ... = The general certainly knows ...
Latin adverbs are flexible in position; certe often appears early, but it could move without changing the core grammar.

Latin comparisons can be made in two common ways: 1) quam + the same case as the thing compared
2) the ablative of comparison (without quam)

Here we have method (1): meliorem ... quam bellum.
Because pacem is accusative in the indirect statement, bellum is also in the accusative after quam.

Yes. You could write:
Imperator certe scit pacem meliorem esse bello.
Here bello is the ablative of comparison, used instead of quam bellum. Both are common; quam is often clearer, especially for learners.

bellum is a 2nd declension neuter noun (bellum, bellī).
Here it is accusative singular, and for neuter nouns the nominative and accusative singular are identical (both bellum).

Yes. Imperator is nominative singular, which marks it as the subject of scit.
Latin often omits subject pronouns, so case endings are key: imperator (nom. sg.) + scit (3rd sg.) match.

• imperator, imperatoris (m.) = commander, general
• scio, scire, scivi, scitum = know
• pax, pacis (f.) = peace
• bonus, -a, -um → comparative melior, melius = better
• sum, esse, fui = be
• bellum, belli (n.) = war
• certe (adv.) = certainly

Comparatives like melior (m/f), melius (n) decline like 3rd declension adjectives.
Accusative singular:

• masculine/feminine: meliorem
• neuter: melius

Since pax is feminine and accusative (pacem), we use meliorem.

Not in this construction. After scit introducing an indirect statement, Latin expects accusative + infinitive, so the “subject” must be accusative: pacem.

• pax (nominative) would fit a direct statement: Pax melior est quam bellum.
• pacis (genitive) would change the meaning (e.g., “of peace”) and wouldn’t work as the subject.

No. Latin usually does not use a separate word for that here. Instead, it uses the accusative + infinitive construction to express “that …”.

Classical Latin typically uses accusative + infinitive after verbs of knowing, thinking, saying, perceiving (scit, putat, dicit, videt, etc.).
Using quod/quia clauses is possible (especially later Latin and in some contexts), but A+I is the standard classical pattern.

esse is the present infinitive. In indirect statement, the infinitive’s tense is relative to the main verb:

• present infinitive = action/state contemporary with scit
  So it means the general knows peace is better (at the same time as his knowing).

Yes, by changing the infinitive:

• pacem meliorem fuisse quam bellum = peace was better (perfect infinitive; prior time)
• pacem meliorem futuram esse quam bellum = peace will be better (future infinitive; later time; futuram agrees with pacem)

Latin word order is flexible and often used for emphasis and rhythm. Imperator certe scit ... places certe early to emphasize the certainty of his knowledge.
Other placements are possible and usually still grammatical, though the emphasis can shift.

Not necessarily. imperator in many Latin contexts means commander / general. It can become emperor as a title in later Roman usage, but the basic sense is “military commander,” and context decides.

Grammatical gender in Latin usually does not affect meaning directly. It mainly affects agreement (adjectives, pronouns, participles).
Here it matters because meliorem must match pacem (feminine), not bellum (neuter).

You’d swap the roles inside the indirect statement and adjust agreement: Imperator certe scit bellum melius esse quam pacem.

• bellum becomes the accusative subject of esse
• comparative becomes neuter accusative melius to match bellum
• pacem becomes the second item in the comparison after quam