Dnes jsme se dohodli, že můj podíl je malý.

Yes. Czech word order is quite flexible, and putting Dnes at the beginning gives today special prominence.

• Dnes jsme se dohodli, že... = Today, we agreed that...
• You could also say Jsme se dnes dohodli, že...

Both are natural, but the first version highlights today more strongly. Czech often moves time expressions toward the front when they set the scene.

Because Czech often leaves out subject pronouns when they are already clear from the verb form.

In jsme se dohodli, the word jsme shows we. So adding my would usually be unnecessary:

• Dnes jsme se dohodli... = Today we agreed...

You could say My jsme se dohodli..., but that would usually add contrast or emphasis, like we agreed.

It is the past tense of dohodnout se / dohodit se? No—here the correct verb is dohodnout se or very commonly dohodnout se / dohodli se in usage, meaning to come to an agreement or to agree.

The form breaks down like this:

• jsme = auxiliary verb to be for we in the past tense
• dohodli = past participle-like form
• se = reflexive particle

So:

• dohodli jsme se = we agreed / we came to an agreement

In this sentence, the order is jsme se dohodli, which is also normal in Czech.

Not really. In this sentence, se is part of the verb dohodnout se / dohodnout se, meaning to agree or to come to an agreement.

So:

• dohodnout without se is not the same basic meaning here
• dohodnout se functions as a reflexive verb

In English, you usually would not translate se separately. You just translate the whole expression:

• dohodli jsme se = we agreed

So se is grammatical and lexical here, not something you usually translate as ourselves.

This tells you something about the group referred to by we.

In the past tense plural, Czech distinguishes gender:

• dohodli = masculine animate plural, or a mixed group that includes at least one male
• dohodly = all-female group, or sometimes non-masculine groups depending on context

So jsme se dohodli suggests that the speakers are:

• either all male,
• or a mixed group with at least one male.

If the speakers were all women, it would normally be:

• Dnes jsme se dohodly, že můj podíl je malý.

Because že introduces a subordinate clause, like that in English.

The sentence has two parts:

• main clause: Dnes jsme se dohodli
• subordinate clause: že můj podíl je malý

Czech normally separates such clauses with a comma:

• ...dohodli, že...

This is standard punctuation.

Very often, yes. In this sentence, že means that and introduces what was agreed:

• agreed that my share is small

It is one of the most common conjunctions in Czech.

In other contexts, že can also appear in expressions with a slightly different feel, but for a learner, that is the main meaning to remember here.

Because můj has to agree with podíl.

Here:

• podíl is masculine singular
• it is in the nominative, because it is the subject of je

So the possessive adjective also appears in masculine singular nominative:

• můj podíl = my share

Compare:

• moje část = my part because část is feminine
• moje auto = my car because auto is neuter

Podíl means something like:

• share
• portion
• stake
• part, depending on context

In this sentence, můj podíl je malý most naturally means:

• my share is small
• my portion is small
• possibly my stake is small

The exact English word depends on context:

• business: stake/share
• division of something: share/portion
• contribution: sometimes part/share

Because malý is an adjective describing podíl, and it has to agree with it.

Since podíl is:

• masculine
• singular
• nominative

the adjective is also:

• masculine
• singular
• nominative

So:

• podíl je malý = the share is small

Compare:

• část je malá = the part is small because část is feminine
• město je malé = the city is small because město is neuter

Yes. It can mean physically small in some contexts, but here it is probably figurative.

So můj podíl je malý could mean:

• my share is small in quantity
• my stake is small
• my contribution is limited
• my role is minor

Czech uses malý both literally and figuratively, just like English small.

Usually the best natural translation is:

• Today we agreed that my share is small.

Czech past tense often covers what English expresses with the simple past. Whether English uses agreed or have agreed depends on context, but in ordinary translation, agreed is the safest choice here.

Also, dohodnout se is a perfective verb, so it refers to a completed agreement.

Because Czech does not have articles.

So Czech simply says:

• můj podíl je malý

and English has to decide whether to use the, a, or no article based on context.

Here, English usually does not need an article before my share, because possessives like my already fill that role.

This is why Czech learners of English and English learners of Czech often notice a big difference here:

• Czech: no articles at all
• English: articles are very important

Yes, to some extent. Czech allows several word orders, though the emphasis changes.

For example:

• Dnes jsme se dohodli, že můj podíl je malý.
• Dnes jsme se dohodli, že je můj podíl malý. — less neutral in most contexts
• Jsme se dnes dohodli, že můj podíl je malý.
• Že můj podíl je malý, jsme se dnes dohodli. — much more marked, not the neutral version

The original sentence is a natural, neutral way to say it. Czech word order often reflects information structure, not just grammar.