Судя по скорости отжима, выбран деликатный режим.

Судя по is a very common fixed expression meaning judging by, based on, or to go by.

So:

• Судя по скорости отжима = Judging by the spin speed / Based on the spin speed

A useful thing to remember is that судя по + dative is a set pattern:

• Судя по всему = judging by everything / apparently
• Судя по его голосу = judging by his voice
• Судя по погоде = judging by the weather

Grammatically, судя originally comes from the verb судить meaning to judge, but in this phrase learners usually just treat судя по as one chunk.

Because судя по requires the dative case.

The basic noun is:

• скорость = speed

Its dative singular form is:

• скорости

So:

• судя по скорости = judging by the speed

This is worth memorizing as a pattern rather than trying to translate word by word every time.

Because скорость is followed by the noun that tells you the speed of what.

• скорость = speed
• отжим = spin cycle / spinning / wringing out

Russian commonly expresses this relationship with the genitive:

• скорость отжима = the speed of the spin cycle / spin speed

This is similar to other combinations like:

• температура воды = water temperature
• цвет машины = the car’s color
• начало фильма = the beginning of the film

So отжима is genitive singular after скорость.

In the context of a washing machine, отжим means the spin cycle or spinning that removes water from the clothes.

So:

• скорость отжима = spin speed

Depending on context, отжим can have other meanings in Russian, but here the washing-machine meaning is the relevant one.

Because выбран is the short form passive participle, used as part of the predicate, while выбранный is the full form, usually used like an adjective before a noun.

Compare:

• Режим выбран. = The mode has been selected.
• Выбранный режим = the selected mode

So in your sentence:

• выбран деликатный режим = the delicate mode has been selected

This is one of the most common things learners notice with Russian participles:
short form = often predicate
full form = often adjective-like modifier

The subject is деликатный режим.

Even though it comes after выбран, it is still the subject because it is in the nominative case and agrees with выбран:

• деликатный режим = masculine singular
• выбран = masculine singular

A more straightforward word order would be:

• Деликатный режим выбран.

But Russian word order is flexible, and Выбран деликатный режим sounds natural too. It can put a little more emphasis on the result or on the fact of selection.

Russian usually does not use a present-tense form of to be the way English does.

So where English says:

• The delicate cycle is selected
• The delicate cycle has been selected

Russian can simply say:

• Деликатный режим выбран

The short passive participle выбран already expresses the idea of a completed selection or resulting state.

If you wanted the past more explicitly, Russian could use:

• Деликатный режим был выбран = The delicate cycle was selected

But in many everyday or technical contexts, выбран alone is enough.

Because Судя по скорости отжима is an introductory/adverbial phrase meaning judging by the spin speed.

In Russian, phrases like судя по... are normally set off with a comma:

• Судя по погоде, будет дождь.
• Судя по его тону, он недоволен.
• Судя по скорости отжима, выбран деликатный режим.

So the comma marks that opening phrase before the main statement.

Literally, режим often means mode or setting. But in the context of a washing machine, natural English often prefers cycle.

So:

• деликатный режим = delicate mode
• very natural English: delicate cycle

Both are possible, but cycle is often what a native English speaker would expect on a washing machine.

Yes, it is effectively a passive-style construction.

• выбрать = to choose/select
• выбран = selected / chosen

So выбран деликатный режим literally means something like:

• the delicate mode is selected
• the delicate mode has been selected

Russian often uses this kind of construction in technical descriptions, interfaces, instructions, and formal statements.

A few good options are:

• Judging by the spin speed, the delicate cycle is selected.
• Based on the spin speed, the delicate cycle has been selected.
• Judging from the spin speed, the delicate mode is selected.

If this is about what setting a washing machine is currently on, the most natural English version is probably:

• Judging by the spin speed, the delicate cycle is selected.

or even more idiomatically:

• The spin speed suggests that the delicate cycle is selected.

Yes. Russian word order is flexible, and several versions are possible:

• Судя по скорости отжима, выбран деликатный режим.
• Судя по скорости отжима, деликатный режим выбран.

Both are grammatical. The difference is mostly about emphasis and style.

• выбран деликатный режим can sound a bit more formal or result-focused
• деликатный режим выбран is a little more straightforward for learners to parse

In real Russian, both patterns are common.