Learn Hardcore Czech: Po večeři myju nádobí a čistím stůl, aby měla maminka méně práce. - After dinner I wash the dishes and clean the table so that mom has less work.

Both versions are correct. Word order in Czech is relatively flexible. Placing Po večeři at the beginning emphasizes the time frame (“as for after dinner…”), while putting it later is more neutral.

All of these are fine, with slight differences in emphasis, not in grammar:

Po večeři myju nádobí… (focus on after dinner)
Myju po večeři nádobí… (focus more on what you do)
Myju nádobí po večeři… (very natural, neutral)

What exactly is the form myju? I thought the verb mýt was irregular; why not myji?

The infinitive is mýt = to wash.

Present tense (1st person singular) has two standard variants:

myji – more formal / standard, often in writing
myju – very common in everyday spoken Czech

So:

(já) myji nádobí – correct, a bit bookish or neutral
(já) myju nádobí – correct, very natural in speech

Both mean “I wash the dishes”.

Full colloquial paradigm (everyday speech) is typically:

já myju
ty myješ
on/ona/ono myje
my myjeme
vy myjete
oni myjou (or myjí in more formal language)

Why is it myju nádobí and not something like myju talíře or “I wash the dishes” literally?

In Czech, nádobí is a mass / collective noun meaning “dishes, crockery, pots, pans, etc.”. It behaves grammatically as a singular neuter noun, even though in English you use a plural (the dishes).

mýt nádobí = to do the dishes / wash up

You can be more specific:

myju talíře – I wash (the) plates
myju hrnky – I wash mugs

But myju nádobí is the default idiomatic way to say “I do the dishes.”

What is the difference between mýt nádobí, umýt nádobí and umývat nádobí?

This is about aspect (imperfective vs perfective).

mýt nádobí – imperfective
- Focus on the activity / process:
- I’m washing / I usually wash the dishes.
umývat nádobí – imperfective, iterative/habitual
- Very close in meaning to mýt nádobí, but often with a “repeated action” feel:
- I (regularly) wash the dishes; I’m in the middle of washing (them).
umýt nádobí – perfective
- Focus on completion / result:
- to wash the dishes (and finish the job), to get the dishes washed.

Examples:

Každý den po večeři myju / umývám nádobí.
I wash the dishes every day after dinner. (habit)
Už jsi umyl nádobí?
Have you already washed (finished washing) the dishes?

Why is it čistím stůl and not something like uklízím stůl or utírám stůl?

All are possible but they have slightly different nuances:

čistím stůl – I clean the table (general cleaning, can include wiping, removing stains, etc.)
utírám stůl – I wipe the table (specifically about wiping, usually with a cloth)
uklízím stůl – I tidy/clear the table (removing plates, putting things away, organizing)

In your sentence, čistím stůl is a general description: you are making the table clean, possibly by wiping and removing crumbs.

If you want to emphasize wiping specifically, utírám stůl is often the most natural choice in everyday speech.

Why is there a comma before aby?

Aby introduces a subordinate clause of purpose (“so that / in order that”), so in Czech spelling rules it must be separated by a comma from the main clause:

Po večeři myju nádobí a čistím stůl, aby měla maminka méně práce.

Main clause:
Po večeři myju nádobí a čistím stůl
Subordinate clause of purpose:
aby měla maminka méně práce

So the comma is compulsory here.

Why is it aby měla maminka méně práce and not aby má maminka méně práce?

After aby Czech normally uses the past tense form of the verb (without any auxiliary like by), which functions like a subjunctive / “so that she will / would have”.

má = present tense she has
měla = past tense form she had, but after aby it often refers to a desired future result.

So:

aby měla maminka méně práce
literally: so that mum had less work, but meaning
→ so that mum has less work / will have less work / will have to do less.

Using aby má is ungrammatical. The pattern is:

aby + (past tense form) to express purpose, wish, or desired result.

E.g.:

Dělám to, aby byl klid.
I do it so that there is peace / so things are calm.

Could I also say aby maminka měla méně práce? Is there any difference from aby měla maminka méně práce?

Both are correct:

aby maminka měla méně práce
aby měla maminka méně práce

Czech word order is flexible. The difference is one of emphasis / focus, not of grammar:

aby maminka měla méně práce – neutral: so that mum has less work.
aby měla maminka méně práce – slight emphasis on maminka; like “so that MUM has less work (not someone else).”

In everyday speech, version 1 is a bit more common, but version 2 is perfectly natural.

Why is méně práce in this form? What case is práce here?

Méně (less) is a comparative quantifier that usually takes the genitive:

méně práce – less work
více času – more time
méně peněz – less money

Here práce is genitive singular (and looks the same as nominative/accusative, which can be confusing).

General pattern for many nouns:

nominative: práce (work)
genitive: práce (of work)

So in méně práce, the genitive is required by méně.

Why is it maminka and not mamince? I thought we sometimes use dative for “for my mum”.

Here maminka is the subject of the verb mít:

maminka měla méně práce
= Mum had less work.

So maminka is in the nominative case (who has less work? Mum does).

If you wanted a structure like “so that there is less work for mum”, you could say:

…aby měla maminka méně práce. – so that mum has less work.
…aby měla méně práce maminka. – same, different emphasis.
…aby měla méně práce pro maminku. – less work for mum (using pro + accusative).

Mamince would be dative and would fit in a different sentence structure, for example:

Aby mamince ubylo práce. – so that mum’s work decreases / so that mum has less work.

But in your original sentence, maminka is simply the grammatical subject.

What is the nuance of maminka compared to máma or matka?

All mean “mother”, but register and tone differ:

maminka – diminutive, affectionate, very common in families and informal situations; often used by children and adults alike in a warm context.
máma – informal, neutral in everyday speech, like mom / mum.
matka – neutral in official or formal language, can sound cold or even harsh in everyday conversation.

In a sentence like yours, maminka sounds warm and family-oriented:

…aby měla maminka méně práce.
→ so that (my) mum has less work (nice, caring tone).

Where is the subject “I”? Why isn’t já written before myju?

Czech is a “pro-drop” language, which means subject pronouns are often omitted when the verb ending already makes the subject clear.

(já) myju nádobí – I wash the dishes.
(ty) myješ nádobí – you wash the dishes.

The -u ending in myju already tells us the subject is 1st person singular (já), so you don’t need to write já unless you want to emphasize it:

Já po večeři myju nádobí…
→ I wash the dishes after dinner (implying not someone else).

In your sentence, the neutral, natural form simply leaves já out.