Illicitator iterum licetur, et licitatio pretium auget.

It is functioning as a nominative singular noun, the subject of licetur.

A learner can tell this because:

• it is the noun doing the action of licetur
• licetur is 3rd person singular, so it needs a singular subject
• the sentence structure naturally gives Illicitator as the bidder

So the first clause is built like:

• Illicitator = subject
• iterum = adverb
• licetur = verb

Because licetur is a deponent verb form.

In Latin, deponent verbs:

• have passive-looking forms
• but carry active meanings

So licetur looks like a passive form, but it means he/she/it bids, not is bidden.

More specifically, licetur is:

• 3rd person singular
• present tense
• indicative mood

from the deponent verb liceor.

Iterum is an adverb meaning again or a second time.

It modifies licetur, so the sense is:

• bids again
• makes another bid

Because it is an adverb, it does not change form for case, number, or gender.

Yes. They belong to the same general word family connected with bidding.

You can think of them like this:

• Illicitator / licitator = bidder
• licetur = bids
• licitatio = bidding, the act/process of bidding

Latin often uses several related words in one sentence like this. It can sound repetitive in English, but in Latin it is perfectly normal and can make the idea very clear.

Licitatio is nominative singular.

It is the subject of auget in the second clause:

• licitatio = the bidding
• auget = raises/increases

So the basic structure is:

• licitatio = subject
• pretium = object
• auget = verb

Here pretium is the direct object of auget.

So the second clause means:

• the bidding raises the price

A point that often confuses learners: pretium is a neuter noun, and neuter nouns have the same form in the nominative and accusative singular. So pretium could in principle be either subject or object by form alone.

Context shows it is the object, because:

• licitatio is already the natural subject
• auget means raises/increases something
• what gets raised is pretium

Auget is:

• 3rd person singular
• present tense
• active voice
• indicative mood

from augeo, augere, meaning to increase, to enlarge, or to raise.

So licitatio pretium auget means the bidding raises the price.

Because Latin normally has no articles.

That means a Latin noun by itself can often be translated as:

• a bidder
• the bidder

depending on context.

So:

• Illicitator can mean a bidder or the bidder
• licitatio can mean bidding or the bidding
• pretium can mean a price or the price

English needs articles much more often than Latin does.

No. Latin word order is fairly flexible because the endings usually show what each word is doing.

This sentence uses a very straightforward order:

• Illicitator iterum licetur
• et licitatio pretium auget

That is roughly:

• subject + adverb + verb
• and
• subject + object + verb

But Latin could rearrange these words for emphasis without changing the basic meaning.

Et simply means and.

It links the two clauses:

• Illicitator iterum licetur
• licitatio pretium auget

So it joins two related statements:

• the bidder bids again
• the bidding raises the price

Many learners would expect licitator, the standard noun meaning bidder.

So if Illicitator looks strange to you, that is a reasonable reaction. In a sentence built around the bidding word family, licitator is the form most people would expect. If your text really prints Illicitator, it may be a spelling issue in the exercise rather than a new grammatical point.

For understanding the sentence, the important thing is that the first word is the subject noun meaning bidder.