Learn Hardcore Japanese: yama de ha sora ga akarukute mo, hosi ga mierukoto ga arimasu. - In the mountains, even when the sky is bright, stars can sometimes be seen.

で marks the location or setting (“at/in the mountains”).
は then turns that locational phrase into the topic and often adds a contrastive nuance (“as for in the mountains…”), implying “as opposed to other places.”

What does the ても form in 明るくても indicate, and how is it formed for different word types?

Why is ことがある used after 見える, and what does this pattern mean?

Verb + ことがある expresses that an action or state occurs occasionally or sometimes.
Here, 星が見えることがある literally means “there are times when you can see stars,” i.e. “sometimes you can see stars.”

Could you use 時 instead of こと in 見えることがある? What’s the difference between 〜ことがある and 〜時がある?

〜ことがある focuses on the occurrence of an event: “it happens occasionally that….”
〜時がある (“ときがある”) highlights particular moments in time when something happens.
In general usage:
• ことがある = sometimes/occasionally (“I sometimes see stars.”)
• 時がある = there are times/moments (“There are times when I look at the sky.”)
For expressing “sometimes you can see stars,” ことがある is more natural.

Why are 空 and 星 both marked with が instead of は in this sentence?

が marks the grammatical subject or the “new” information in subordinate clauses and existential or perceptual verbs like 見える.
空が明るい states a descriptive fact about the sky.
星が見える emphasizes that stars become visible (new information).
Replacing が with は would shift the focus or imply a contrast you may not intend.

Why can’t we drop ことがある and just say 山では空が明るくても星が見える?

Without ことがある, you’d assert as a general truth that “even if the sky is bright in the mountains, stars are visible,” suggesting they’re visible all the time under that condition.
ことがある adds “sometimes/occasionally,” softening it to “there are occasions when…,” which matches the intended nuance of occasionally seeing stars in a bright sky.