haha ha kesyou ga owattara, eki mae no kafe he dekaketa.

They are doing different jobs.

• 母は marks the topic: the sentence is about the mother.
• 化粧が marks the subject of the smaller clause 化粧が終わったら.

Japanese often has a topic in the main sentence and a separate subject inside a subordinate clause. So this is not a contradiction or double-subject mistake.

Because 終わる is an intransitive verb, so it normally goes with が, not を.

• 化粧が終わる = the makeup is finished / the makeup is done
• 化粧を終える = to finish the makeup

So if you want を, you would normally use 終える instead:

• 化粧を終えたら

In everyday Japanese, 化粧が終わる is very natural.

The person is not stated explicitly, but it is understood from context to be the mother.

Grammatically, 化粧 is the subject of 終わる, so the Japanese is structured more like:

• when her makeup was done
• after the makeup was finished

In natural English, we often translate that as after she finished her makeup, even though Japanese phrases it differently.

Here it is giving a time sequence, not a real if condition.

• 終わったら here means when it was finished, after finishing, or once it was done

Because the main verb is past tense (出かけた), the sentence describes what happened next in the past.

So in this sentence, 〜たら is best understood as:

• after
• when
• once

not as a hypothetical if.

化粧 is a noun meaning makeup or cosmetics, but in context it often refers to putting on makeup or one’s makeup routine.

So 化粧が終わる does not mean the cosmetics themselves somehow end. It means:

• one’s makeup is finished
• one is done putting on makeup

This is a very common kind of Japanese expression.

駅前 is a set compound word meaning the area in front of or around the station.

So:

• 駅前のカフェ = a café in the station-front area / near the station

By contrast:

• 駅の前 is more literal: right in front of the station

So 駅前 often sounds a little more like a place name or general area, while 駅の前 sounds more physically exact.

The の links 駅前 and カフェ, so it works like the café of the station-front area or more naturally:

• the café near the station
• the station-front café

It is just the standard noun-linking の.

Yes, に would also be possible here.

With motion verbs like 出かける, both へ and に can mark where someone goes:

• カフェへ出かけた
• カフェに出かけた

The difference is small:

• へ emphasizes the direction or heading toward a place
• に emphasizes the destination

In many everyday sentences, they are very close in meaning.

出かける means to go out, often with the nuance of leaving where you are (especially home) to go somewhere.

• 行く = to go
• 出かける = to go out

So カフェへ出かけた suggests something like:

• she went out to the café
• she headed out for the café

It feels a little more natural than 行った if the image is of the mother leaving home after getting ready.

Yes, 母 usually refers to one’s own mother when speaking to others or in narration.

A useful distinction is:

• 母 = my mother (plain/reference form)
• お母さん = mom / mother when addressing her directly, or sometimes when referring to someone else’s mother

So in an isolated example sentence, 母 is perfectly natural and is usually understood as my mother or simply mother, depending on context.