V autobuse je dnes moc lidí, proto půjdu do práce pěšky.

Czech normally uses v with enclosed spaces and vehicles when you mean inside them.

• v autobuse = in/on the bus
• v autě = in the car
• ve vlaku = on the train

English often says on the bus, but Czech usually says v autobuse.

na autobuse would usually sound like on top of the bus, not riding the bus.

Because the preposition v (when it means in) requires the locative case.

• dictionary form: autobus
• locative singular: autobuse

So:

• v autobuse = in/on the bus

This is a normal case change after certain prepositions.

This is very common in Czech with quantity expressions like:

• moc
• hodně
• málo
• dost

With these, Czech usually uses 3rd person singular:

• Je moc lidí. = There are a lot of people.
• Bylo hodně aut. = There were a lot of cars.

So even though lidí refers to many people, the whole phrase moc lidí behaves like a quantity expression, and je is the normal form here.

After quantity words like moc, the noun usually goes into the genitive plural.

• nominative plural: lidé = people
• genitive plural: lidí

So:

• lidé = people (as the subject in a regular plural sentence)
• moc lidí = many/a lot of people

Compare:

• Lidé čekají. = People are waiting.
• Je tam moc lidí. = There are a lot of people there.

Here moc means a lot of / many.

So moc lidí = a lot of people / many people.

Depending on context, it can also feel like too many people. In this sentence, because the speaker then decides to walk to work, English may naturally translate it as too many people.

Also, moc can have another use in Czech:

• moc hezký = very pretty (colloquial)
• moc lidí = many/a lot of people

So it is the same word, but used differently.

Because Czech often drops subject pronouns when the verb ending already shows who is doing the action.

• půjdu = I will go

The ending tells you it is 1st person singular, so já is not necessary.

You can add já if you want emphasis or contrast:

• Já půjdu do práce pěšky. = I will walk to work.

But in a neutral sentence, leaving it out is more natural.

Because jít is one of the Czech verbs that forms the future irregularly.

• present: jdu = I am going
• future: půjdu = I will go

Czech does not normally say budu jít.

This is especially common with verbs of motion. So you simply learn:

• jít → půjdu
• jet → pojedu

Also, půjdu here refers to one specific trip: this time, today, I will go on foot.

Because do expresses motion to / into a place and takes the genitive case.

• do práce = to work
• do školy = to school
• do města = to the city

Here práce is the genitive singular form of práce.

This is also a very common fixed expression:

• jdu do práce = I’m going to work
• jsem v práci = I’m at work

No, here pěšky is an adverb, and it means on foot.

So:

• jít pěšky = to go on foot / to walk

It does not change for case, gender, or number here. It is just a fixed adverbial form.

Compare:

• autobusem = by bus
• vlakem = by train
• pěšky = on foot

Proto means therefore / so / for that reason.

It connects the first idea to the result:

• There are a lot of people on the bus today,
• therefore / so I’ll walk to work.

It is a very common linking word in Czech.

Because proto introduces the second clause, which is logically connected to the first one.

So Czech writes:

• V autobuse je dnes moc lidí, proto půjdu do práce pěšky.

This is similar to English punctuation in sentences like:

• There are too many people on the bus today, so I’ll walk to work.

Yes. Czech word order is fairly flexible.

For example, you could also say:

• Dnes je v autobuse moc lidí, proto půjdu do práce pěšky.

That still means the same thing.

The version V autobuse je dnes moc lidí starts with v autobuse to set the scene first: on the bus / in the bus.
Czech often moves words around for emphasis, topic, or flow, not because the basic grammar changes.