Codicilli patrimonium mancipatum ostendunt.

The main clue is the verb ostendunt.

• ostendunt = they show
• The ending -unt tells you the verb is 3rd person plural

So you look for a nominative plural noun to match that verb, and codicilli fits that role.

Meanwhile:

• patrimonium is accusative singular, so it is the direct object
• mancipatum agrees with patrimonium, so it also belongs with the object, not the subject

So the basic structure is:

• codicilli = subject
• patrimonium mancipatum = object
• ostendunt = verb

Yes. In isolation, codicilli can be either:

• nominative plural = codicils / little books
• genitive singular = of the codicil / of the little book

But in this sentence, the verb ostendunt is plural, so we need a plural subject. That makes codicilli nominative plural here.

If it were genitive singular, the sentence would need a different structure to make sense grammatically.

Patrimonium is accusative singular neuter.

That tells you it is the direct object of ostendunt.

So whatever the codicils are doing, they are doing it to or with patrimonium in the sense that they are showing it.

This is a very common Latin pattern:

• nominative subject
• accusative direct object
• finite verb

Mancipatum is a perfect passive participle from mancipare.

In this sentence it modifies patrimonium and means something like:

• transferred
• conveyed
• formally alienated
• in a specifically legal sense, transferred by mancipatio

So patrimonium mancipatum means the transferred estate/inheritance or the estate that has been formally transferred.

Because it has to agree with patrimonium.

Patrimonium is:

• neuter
• singular
• accusative

So the participle modifying it must also be:

• neuter
• singular
• accusative

That gives mancipatum.

This is standard adjective/participle agreement in Latin: modifiers agree with the nouns they describe in gender, number, and case.

Because mancipatum is being used adjectivally, not as the main verb of a passive clause.

Compare these two ideas:

• patrimonium mancipatum = the transferred estate
  Here the participle just describes the noun.

• patrimonium mancipatum est = the estate has been transferred
  Here the participle plus est forms a full passive verb.

In your sentence, the main verb is already ostendunt, so mancipatum is simply modifying patrimonium.

Ostendunt is:

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

Its dictionary form is ostendo, ostendere, ostendi, ostentum.

So grammatically it means they show or they are showing, depending on context.

Not especially. Latin word order is much more flexible than English word order.

Here you have:

• Codicilli = subject
• patrimonium mancipatum = object with modifier
• ostendunt = verb

A very natural literal layout is:

• The codicils the transferred estate show

In smoother English, of course, you rearrange it.

Latin often puts the verb at or near the end, and it often places a participle after the noun it modifies, so this word order is quite normal.

It is more technical than ordinary handed over.

The verb mancipare belongs to the language of Roman legal transfer. It refers to a formal kind of conveyance called mancipatio.

So depending on context, mancipatum may be translated more loosely as:

• transferred
• conveyed
• assigned

But in a legal or historical context, it often carries the sense of a formal legal transfer, not just casual giving.

Because Latin has no articles.

So Latin does not normally have separate words for:

• the
• a / an

Whether you translate a noun as definite or indefinite depends on context.

For example:

• codicilli could be codicils or the codicils
• patrimonium could be an estate, the estate, inheritance, or the inheritance

English has to choose; Latin usually does not mark that explicitly.

They are:

• codicillus, codicilli = codicil, little book, notebook
• patrimonium, patrimonii = patrimony, inherited estate, property
• mancipo, mancipare, mancipavi, mancipatum = to transfer formally, to convey by legal act
• ostendo, ostendere, ostendi, ostentum = to show, display, reveal

Knowing the dictionary form helps you identify the declension or conjugation and understand why the word has the form it does in the sentence.

Yes, that is a very good way to read it.

You can group the sentence like this:

• Codicilli | patrimonium mancipatum | ostendunt

Inside that middle group:

• patrimonium = the noun
• mancipatum = the participle describing it

So the participle is not doing a separate action on its own. It is part of a noun phrase: the transferred inheritance/estate.

That kind of grouping is very useful when reading Latin.