Водитель сказал, что до центра можно доехать без пересадки за двадцать минут.

The preposition до normally requires the genitive case.

So:

• центр = the center
• до центра = to the center / as far as the center

This is a very common pattern:

• до дома = to home / as far as the house
• до вокзала = to the station
• до конца = to the end

In this sentence, до центра means reaching the city center as a destination.

Доехать is a perfective verb that focuses on successfully reaching a destination.

Compare:

• ехать = to be going / to go by transport
• доехать = to get there / to reach by transport

Because the sentence is about whether it is possible to reach the center, Russian uses доехать.

So:

• можно ехать would sound more like it is possible to be going / to travel
• можно доехать means it is possible to get there

That makes доехать the natural choice here.

This is an impersonal construction.

• можно = it is possible / one can
• доехать = get there by transport

So можно доехать means:

• you can get there
• it’s possible to get there
• one can reach it

There is no specific subject like you or we in the Russian sentence. Russian often leaves that general subject unstated in this kind of construction.

Без always takes the genitive case, so:

• пересадка = transfer / change
• без пересадки = without a transfer / without changing

This phrase is very common in travel Russian.

Examples:

• ехать без пересадки = to travel without changing
• добраться без пересадки = to get there without a transfer

So here it means the trip to the center can be done directly, without changing buses, trains, etc.

Here за + accusative expresses the time needed to complete an action.

So:

• за двадцать минут = in twenty minutes

Because доехать is perfective, the phrase means the destination can be reached within a total time of twenty minutes.

Compare:

• за двадцать минут = in twenty minutes, finish within that time
• двадцать минут = for twenty minutes
• в течение двадцати минут = during twenty minutes
• через двадцать минут = in twenty minutes from now

So за двадцать минут is the correct choice for how long it takes to get there.

Сказал is the perfective past of сказать, and it usually means said as a completed act.

• сказать / сказал = to say / said
• говорить / говорил = to speak / was saying / used to say

In this sentence, the driver made one specific statement, so сказал is the most natural verb.

If you used говорил, it could sound more like:

• he was talking
• he used to say
• he was in the process of saying

For reported speech with one concrete remark, сказал, что... is very standard.

Because что introduces a subordinate clause:

• Водитель сказал = The driver said
• что до центра можно доехать... = that it is possible to get to the center...

In Russian, subordinate clauses introduced by что are separated by a comma.

So the structure is:

• main clause + comma + subordinate clause

This is normal Russian punctuation.

Usually, сказал is the masculine past-tense form, so yes, the sentence as written suggests a male driver.

Russian past tense agrees with gender in the singular:

• сказал = he said
• сказала = she said
• сказало = it said
• сказали = they said

So if the driver were female, you would usually expect:

• Водитель сказала, что...

Even though водитель itself is a noun commonly used for both male and female drivers, the past-tense verb shows the gender.

Yes. Russian word order is fairly flexible, though different orders can change the emphasis.

The neutral version here is:

• Водитель сказал, что до центра можно доехать без пересадки за двадцать минут.

Other possible orders include:

• Водитель сказал, что без пересадки до центра можно доехать за двадцать минут.
• Водитель сказал, что за двадцать минут можно доехать до центра без пересадки.

These are still understandable, but the original order sounds natural and neutral.

Russian often moves pieces around to highlight:

• destination
• method
• time
• contrast

This is a useful nuance.

• в центр = into the center / to the center
• до центра = up to the center / as far as the center

In many real-life contexts, they may be translated similarly as to the center, especially when talking about transportation.

But доехать до центра is a very common expression meaning to get as far as the center. It focuses on reaching that point as a destination.

So in travel-related Russian, доехать до + genitive is extremely common:

• доехать до станции
• доехать до метро
• доехать до центра

Mostly, yes. Доехать usually means reaching a place by some kind of transport:

• car
• bus
• train
• taxi
• bike, sometimes depending on context

That fits this sentence well, because the speaker is a driver and the phrase без пересадки strongly suggests public transport or a route involving vehicles.

If you were talking about reaching a place on foot, Russian would more naturally use дойти:

• До центра можно дойти за двадцать минут. = You can walk to the center in twenty minutes.

So доехать is the right verb here because the movement is by transport.