Learn Hardcore Korean: jeoneun siktageseo sukjereul haeyo.

저 means “I” in a polite/humble way. The particle -는 is the topic marker, so 저는 translates roughly to “As for me….” In contrast, -가 (as in 제가) is the subject marker that highlights “I” as new or focused information. Using 저는 is more natural when you’re simply stating something about yourself (e.g., your habits or preferences).

Why is 식탁에서 used to say “at the table”? Could I use 식탁에 instead?

The particle -에서 indicates the location where an action occurs. Since you’re doing homework there, you need 식탁에서 (“at the dining table”). The particle -에 marks static location (where something is) or a direction/endpoint (to/into). Saying 식탁에 숙제를 해요 would be ungrammatical because you’re not moving homework to the table—you’re doing it there.

Why do we say 숙제를 해요 rather than just 숙제해요?

The verb is 숙제하다 (“to do homework”). In Korean you separate the noun 숙제 and the verb 하다, and you must attach the object marker -를 (because 숙제 ends in a vowel) to show it’s the direct object. Hence 숙제를 해요. In very casual writing or speech you might see 숙제해요 as one word, but the particle -를 is still understood.

Can I change the word order, for example, 저는 숙제를 식탁에서 해요?

Yes. Thanks to the particles, both 숙제 and 식탁 are clearly marked, so swapping them doesn’t change the meaning. For example, 저는 숙제를 식탁에서 해요 is perfectly fine. Just remember that in a neutral statement the verb (해요) typically comes at the end.

What level of speech is 해요, and what about 합니다 or 해?

해요 is the polite informal style (the “-요” form) used with strangers, acquaintances, or anyone you want to show a polite distance to.
합니다 is the formal polite style (often used in presentations, announcements, or with superiors).
해 is the plain/intimate style used among close friends or when speaking to someone younger.

Can I drop 저는 and simply say 식탁에서 숙제를 해요?

Yes. Korean often omits the topic or subject when it’s clear from context. If your listener knows you’re talking about yourself, 식탁에서 숙제를 해요 is enough to mean “I do my homework at the table.”

What’s the difference between 식탁 and 테이블? Can I say 테이블에서 숙제를 해요?

식탁 literally means “meal table” (dining table) and is the most natural word for a home dining table.
테이블 is a loanword for “table” in general (e.g., café table, study table).
You can say 테이블에서 숙제를 해요 and be understood—just choose the noun that fits your context.

Is 해요 here the simple present (habitual) or present progressive (“I am doing”)? How would I say “I am doing my homework right now at the table”?

In Korean, the simple present tense with 해요 covers both habitual (“I do homework…”) and ongoing actions (“I am doing homework…”). To emphasize “right now,” you can add 지금:
저는 지금 식탁에서 숙제를 해요.
Or use the progressive construction -고 있다:
저는 식탁에서 숙제를 하고 있어요.