Learn Hardcore Japanese: onazi anime wo nikaime ni miru toki ha, zimaku nasi de mite, dorekurai kikitoreru ka tamesite imasu. - When I watch the same anime a second time, I watch it without subtitles and test how much I can catch.

So the object アニメ still needs を, even though there are other words (like 二回目に) in between. In Japanese it’s normal to put adverbs and time expressions between the object and the verb.

Why is 二回目 followed by に? What does 二回目に mean exactly?

二回目 means the second time (an ordinal: first time, second time, etc.).

The particle に here marks a specific occasion/instance:

二回目に見る = to watch (it) on/for the second time

You can think of に as “on that occasion” or “at that time (number)”.
Compare:

二回見る = to watch it twice (focus on the total number of times)
二回目に見る = to watch it the second time (focus on which time/turn)

Why is 見る in plain dictionary form before とき instead of 見ます or 見た?

Before とき, verbs normally appear in plain form (dictionary or past), even in polite sentences. The form before とき changes the time meaning:

見るとき = when I watch (it) / when I am about to watch (it) (not yet done, or in progress)
見たとき = when I watched (it) / when I had watched (it) (already done)

Here the meaning is “when I watch the same anime for the second time”, so 見るとき (non‑past) is appropriate.
Using 見ますとき is grammatically possible but sounds stiff; natural Japanese uses the plain form before とき even in polite speech.

What is the role of は after とき in 見るときは?

は here is the topic marker attached to the entire 見るとき phrase:

(同じアニメを二回目に見るとき) は …
= As for (when I watch the same anime for the second time), …

This sets the situation as a topic and implies contrast:
“In that case (when it’s the second viewing), I do X (but maybe I do something different the first time).”

So ときは often has a nuance like “when it comes to times when … / in the case when …”.

What exactly does 字幕なしで mean? How is it different from 字幕がない or 字幕をつけないで?

字幕 = subtitles
なし = without / none (a noun meaning “absence”)
字幕なしで = with no subtitles / without subtitles, literally “in the state of having no subtitles”, with で marking manner/state.

Comparisons:

字幕なしで見る
- watch without subtitles (you choose that “mode”)
字幕がない
- there are no subtitles (a factual statement about availability, not necessarily your choice)
字幕をつけないで見る
- watch without turning on subtitles (focuses more on the action of not adding/activating them)

In your sentence, 字幕なしで nicely expresses the viewing condition or style.

Why is there another 見て later in the sentence? Isn’t 見る already used in 見るとき?

The first 見る is inside the とき clause:

同じアニメを二回目に見るとき
= when I watch the same anime for the second time

The second 見て is the main action of the sentence:

字幕なしで見て、どれくらい聞き取れるか試しています。
= I watch it without subtitles and test how much I can catch.

So structurally:

When I watch the same anime for the second time,
I watch it without subtitles, and
I test how much I can understand.

The two 見る are in different clauses and play different roles: one sets the condition (とき), the other is what you actually do in that situation.

Why is it 見て、どれくらい聞き取れるか試しています and not something like 見ます。そして試します?

The て-form (見て) is used to link actions smoothly:

字幕なしで見て、どれくらい聞き取れるか試しています。
= I watch without subtitles and (then) test how much I can catch.

Using the て-form shows a natural sequence or connection between actions in one flowing sentence.
You could say:

字幕なしで見ます。そして、どれくらい聞き取れるか試します。

That is grammatically fine but sounds more formal and choppy. Native speech very commonly uses Vて、Vて… to connect sequential actions.

How does どれくらい聞き取れるか試しています work grammatically?

Breakdown:

聞き取れる = can catch / can understand by listening (potential form)
どれくらい聞き取れるか = how much I can catch
- か marks an indirect question (“how much … ?”)
試しています = am trying / am testing

So the structure is:

X か試す = to test/try (to see) whether/how X

In English word order:
どれくらい聞き取れるか試しています ≈ I’m testing how much I can understand (by listening).

Why use 聞き取れる instead of 聞き取る?

聞き取る means “to catch (something) by listening; to make out what is said”.
聞き取れる is the potential form: “to be able to catch; can make out”.

Here the meaning is “how much I am able to catch”, so the potential form is natural:

どれくらい聞き取るか
= how much I catch (factual description of what happens)
どれくらい聞き取れるか
= how much I can catch (focus on your listening ability)

Because this is about testing listening skill, 聞き取れる fits better.

What nuance does 試しています (～ている) have here? Is it “I am testing” right now or “I (habitually) test”?

～ている can mean:

progressive (doing right now), or
habitual / repeated action.

In this sentence, the whole structure 同じアニメを二回目に見るときは…試しています describes a habit/routine:

When I watch the same anime the second time, I (always) watch without subtitles and test my listening.

So 試しています is polite present tense describing a regular practice, not just something you’re doing at this exact moment.

Could I add を after か and say どれくらい聞き取れるかを試しています? Is that wrong?

You can say:

どれくらい聞き取れるかを試しています。

Grammatically it’s fine. Here, どれくらい聞き取れるか is a noun clause, and を marks it as the object of 試す:

I am testing *(the question of) how much I can catch.*

In everyday Japanese, か alone is very often enough:

どれくらい聞き取れるか試しています。

Omitting を makes the sentence a bit lighter and is very natural. Both forms are acceptable; the version without を is more common in casual/politer spoken style.

Is it okay to use 二度目 instead of 二回目? Is there any difference?

Yes, you can say:

同じアニメを二度目に見るときは、…

二度目 and 二回目 are very close in meaning: second time.

Nuance:

回 is a neutral counter for times/occurrences.
度 can feel a bit more literary or formal in some contexts, but in everyday speech 一度 / 二度 are very common too.

In this sentence, 二回目 and 二度目 are both natural. There’s no big change in meaning.

Why is 同じ placed before アニメ? Can it come after, like in English?

Japanese adjectives and adjective‑like words generally go before the noun they modify:

同じアニメ = the same anime
面白いアニメ = an interesting anime

You can’t say アニメ同じ in standard Japanese to mean “the same anime”. (There are structures like アニメが同じ, but that’s a full clause: the anime is the same.)

So the correct noun phrase order is always:

[modifier] + [noun] → 同じアニメ

The sentence mixes plain forms (見る, 聞き取れる) with polite 試しています. Is that allowed?

Yes. In Japanese, subordinate clauses (like those before とき, or inside ～か clauses) almost always use plain form, even when the main clause is polite.

Here:

同じアニメを二回目に見るとき → plain form 見る before とき
どれくらい聞き取れるか → plain form 聞き取れる before か
Main clause: 試しています → polite ます‑form

This combination is completely natural:

X ときは、Y ます。
X か試します。

So there is no politeness mismatch; this is standard polite Japanese.