W tych okolicznościach roślina więdnie.

Because the preposition w can take different cases depending on meaning.

• w + locative = in / at / under a place, situation, or circumstances
• w + accusative = into something, usually with movement

Here the phrase means in/under these circumstances, so Polish uses the locative:

• w tych okolicznościach

If there were movement into something, accusative could appear, but that is not what is happening here.

It is locative plural.

Breakdown:

• okoliczności = circumstances
• after w with the meaning in/under, the noun goes into the locative
• plural locative of okoliczności is okolicznościach
• tych matches the noun in case and number

So:

• nominative plural: te okoliczności
• locative plural: w tych okolicznościach

Because tych is the form required by the locative plural.

The base form is:

• te okoliczności = these circumstances

But after w in this meaning, both words change:

• w tych okolicznościach

So te changes to tych, and okoliczności changes to okolicznościach.

Roślina is in the nominative singular, because it is the subject of the sentence.

• roślina = plant
• it is the thing doing the action of wilting

So the structure is:

• W tych okolicznościach = adverbial phrase
• roślina = subject
• więdnie = verb

Więdnie is the 3rd person singular present tense form of the verb więdnąć.

So:

• ja więdnę = I am wilting
• ty więdniesz = you are wilting
• on/ona/ono więdnie = he/she/it wilts / is wilting

Because roślina is singular, we use więdnie.

In Polish, just like in English, the present tense can describe:

• something happening now
• a general fact
• a regular tendency
• a process

So roślina więdnie can mean:

• the plant is wilting
• the plant wilts
• the plant tends to wilt

In this sentence, it sounds like a general statement: under these circumstances, a plant wilts.

Więdnąć is imperfective.

That makes sense because wilting is a process, not a single completed act.

Imperfective verbs are used for:

• ongoing actions
• repeated actions
• general truths
• present tense statements

That is why więdnie works naturally here.

A completed-result idea would usually need a different expression, depending on context.

Yes. Polish word order is flexible.

The sentence:

• W tych okolicznościach roślina więdnie.

could also be:

• Roślina więdnie w tych okolicznościach.

Both are grammatical, but the emphasis changes a little.

• W tych okolicznościach roślina więdnie puts emphasis first on the circumstances
• Roślina więdnie w tych okolicznościach starts with the plant and sounds a bit more neutral in some contexts

Starting with the prepositional phrase is very natural when you want to frame the situation first.

Yes, that is a very good translation.

It can also be understood as:

• under these circumstances
• in these conditions

However, there is a nuance worth noticing:

• okoliczności often refers to circumstances in a somewhat broad or formal sense
• warunki often refers more directly to conditions, especially physical conditions

So with a plant, Polish speakers might also say:

• W tych warunkach roślina więdnie. = In these conditions, the plant wilts.

That can sound a bit more concrete and scientific.

Because Polish often uses okoliczności in the plural when talking about a set of surrounding circumstances.

Compare:

• okoliczność = a circumstance, a single circumstance
• okoliczności = circumstances

In practice, the plural is very common in phrases like:

• w tych okolicznościach = in these circumstances
• w takich okolicznościach = in such circumstances

So the plural here is completely natural.

A rough guide is:

• więdnie ≈ vyend-nye

A few helpful points:

• w in Polish sounds like English v
• ię before another consonant often sounds roughly like ye with some nasal quality
• dn in dnie is pronounced smoothly together
• the final -nie sounds like nye

It is not pronounced like English weed-knee or wendie.

A more careful approximation is something like:

• VYEND-nye

with the stress on the second-to-last syllable, as usual in Polish.

A rough approximation is:

• o-ko-LEECH-no-shchyakh

Helpful pieces:

• cz sounds like English ch in chop
• ś is a soft sh sound
• ci before a vowel often gives a soft ć-like sound
• ch sounds like a hard h/kh

The stress is on the second-to-last syllable:

• o-ko-licz-NOŚ-ciach

Polish spelling here looks intimidating, but it becomes easier once you learn the common sound patterns.

Because Polish has no articles.

English distinguishes:

• a plant
• the plant

Polish usually just says:

• roślina

The definite or indefinite meaning is understood from context.

So roślina can mean:

• a plant
• the plant

Depending on the situation, English translation chooses the most natural option.

It could be either, depending on context.

• If you are talking about a specific plant you can see, it may mean the plant wilts
• If you are making a general statement, it may mean a plant wilts

Because Polish has no articles, the sentence itself does not force one interpretation. Context does that.