W poniedziałek jadę metrem do pracy, bo autobus często jest spóźniony.

In Polish, w covers both in and on in many contexts.

So:

• w domu = in the house / at home
• w poniedziałek = on Monday

With days of the week, Polish uses w where English uses on. So w poniedziałek is the normal way to say on Monday.

It is in the accusative.

The expression w + day of the week usually takes the accusative when it means on a particular day:

• w poniedziałek = on Monday
• w piątek = on Friday

For poniedziałek, the accusative looks the same as the nominative because it is a masculine inanimate noun.

So:

• nominative: poniedziałek
• accusative: poniedziałek

Polish very often uses the present form of an imperfective verb to talk about a planned or arranged future.

So jadę literally looks present, but in context it can mean:

• I’m going
• I’m going to go
• I’m taking

Because W poniedziałek already gives a future time, jadę is naturally understood as future here.

This is very common in Polish, especially with verbs of movement:

• Jutro jadę do Krakowa. = I’m going to Kraków tomorrow.
• Wieczorem idę do kina. = I’m going to the cinema this evening.

This is an important motion-verb difference.

• jadę comes from jechać and usually refers to one specific trip or a trip in progress
• jeżdżę comes from jeździć and usually refers to repeated/habitual travel

So:

• W poniedziałek jadę metrem do pracy = On Monday I’m taking the metro to work
  one planned trip, this Monday
• W poniedziałki jeżdżę metrem do pracy = On Mondays I go to work by metro
  habitual action

So the singular w poniedziałek fits well with jadę.

Because Polish often drops subject pronouns when they are not needed.

The ending -ę in jadę already tells you the subject is I.

So:

• jadę = I am going / I’m going
• ja jadę = I am going with extra emphasis, contrast, or clarification

You would use ja only if you want to stress it:

• Ja jadę metrem, a on autobusem. = I’m taking the metro, and he’s taking the bus.

Because Polish uses the instrumental case to express the means of transport after verbs like jechać.

So:

• jadę metrem = I’m going by metro
• jadę autobusem = I’m going by bus
• jadę pociągiem = I’m going by train
• jadę samochodem = I’m going by car

The noun metro changes like this:

• nominative: metro
• instrumental: metrem

That is why you get metrem.

Because do means to in the sense of movement toward a place, and do takes the genitive case.

The noun changes like this:

• nominative: praca = work
• genitive: pracy

So:

• do pracy = to work

Compare:

• Idę do pracy. = I’m going to work.
• Jestem w pracy. = I’m at work.

So do pracy shows direction or destination.

Yes, you could.

• bo = because
• ponieważ = because / since

The difference is mostly style:

• bo is very common, everyday, and natural in speech
• ponieważ is a bit more formal or written

So both are correct:

• Jadę metrem do pracy, bo autobus często jest spóźniony.
• Jadę metrem do pracy, ponieważ autobus często jest spóźniony.

In normal conversation, bo is often the more natural choice.

Yes, and that is a very good question.

Both are possible, but they are slightly different in feel:

• autobus często jest spóźniony = the bus is often late / delayed
• autobus często się spóźnia = the bus often runs late

The version with jest spóźniony describes a state: the bus is in a delayed condition.

The version with się spóźnia describes the action/habit of being late and often sounds especially natural when talking about something that happens repeatedly.

So in everyday Polish, many speakers might also say:

• ...bo autobus często się spóźnia.

The sentence you were given is still correct and understandable.

Because it has to agree with autobus.

Autobus is:

• masculine
• singular
• nominative

So the adjective/past-participle form also has to be:

• masculine
• singular
• nominative

That gives:

• autobus jest spóźniony

Compare:

• kobieta jest spóźniona = the woman is late
• dziecko jest spóźnione = the child is late
• pociągi są spóźnione = the trains are late

Yes. Polish word order is more flexible than English, though some orders sound more neutral than others.

The original sentence is very natural:

• W poniedziałek jadę metrem do pracy, bo autobus często jest spóźniony.

You could also say:

• W poniedziałek jadę do pracy metrem, bo autobus często jest spóźniony.
• Jadę w poniedziałek metrem do pracy, bo autobus często jest spóźniony.

These are all understandable, but the emphasis changes a little.

For example:

• W poniedziałek at the start emphasizes the time
• metrem later in the sentence sounds a bit more neutral
• moving często can slightly shift what is emphasized

So yes, word order is flexible, but the original version is a very good standard one.

Because Polish has no articles.

English uses:

• the metro
• the bus
• a bus
• work

Polish usually leaves this information to context:

• metrem
• autobus
• pracy

So autobus can mean:

• the bus
• a bus

and context tells you which makes sense.

In this sentence, English naturally translates it as the bus because the speaker probably means the usual bus they take to work.

Usually no. If you mean every Monday / on Mondays, Polish normally uses the plural day name and often a habitual verb.

So:

• W poniedziałek jadę metrem do pracy. = This Monday I’m taking the metro to work.
• W poniedziałki jeżdżę metrem do pracy. = On Mondays I go to work by metro.

That difference is very useful:

• singular day: w poniedziałek = on Monday, one specific Monday
• plural day: w poniedziałki = on Mondays, repeatedly

So if the meaning is habitual, the more natural Polish is usually W poniedziałki jeżdżę...