Learn Hardcore Japanese: watasi ha asa ni meeru wo kakuninsimasu.

は is the topic marker (pronounced “wa”). It tells the listener that 私 (“I”) is the topic of the sentence—what you’re going to talk about. It’s not the subject in the strict grammatical sense, but it sets the frame: “As for me, …”

Why is に used after 朝? Can I say 私は朝メールを確認します instead?

に marks a specific point in time (“at/in the morning”).

朝に = “in the morning” (more precise time).
If you drop に, it’s still understandable, but less natural when you want to emphasize exactly when you check your mail.
For habitual actions, you could also say 毎朝 (“every morning”) instead.

What does を do in メールを確認します?

を marks the direct object of the verb. Here, メール is what you check (the thing receiving the action), so you attach を to show “(I) check the email.”

Why is 私 explicitly included? Isn’t the subject often omitted in Japanese?

Yes, Japanese frequently omits the subject when it’s clear from context. Including 私 here adds clarity or emphasis (“As for me, I check my mail…”). In a conversation where it’s obvious who you’re talking about, you could just say 朝にメールを確認します.

Is 確認します the only way to say “check”? What about チェックします?

確認します is a native-Japanese verb meaning “to confirm/check” and is more formal.
チェックします is a loanword from English, more casual/business-like.
Both are common, but 確認します sounds slightly more polite and neutral.

How would I change this sentence to past tense or make it more casual?

Past polite:
　私は朝にメールを確認しました。
Casual present:
　（僕／私）は朝にメールを確認する。
Or drop both 私 and に for a very casual feel:
　朝メール確認する。

How do I say “every morning” instead of just “in the morning”?

Use 毎朝 (“every morning”):
　私は毎朝メールを確認します。
This emphasizes the habitual nature of the action.