Сегодня мне плохо, поэтому я остаюсь дома.

Because плохо here is used as a state (“I feel bad / I’m unwell”), and Russian commonly expresses states with a dative person + category-of-state word:

• мне (to me / for me) + плохо (bad, unwell)
  So мне плохо = “I’m not feeling well.”

Я плохо is incomplete; it would need a verb or be part of something like я плохо себя чувствую (“I feel bad”).

Literally, плохо is “badly,” but in this structure (мне плохо) it means “I feel bad / I’m unwell.” It’s broader than “sick” and can cover:

• illness
• nausea, weakness
• emotional distress
  If you want explicitly “I’m sick (ill),” you might say я болею or я болен/больна.

The dative marks the experiencer of a state in many Russian expressions:

• мне холодно (I’m cold)
• мне жарко (I’m hot)
• мне грустно (I’m sad)
• мне плохо (I feel unwell)
  So мне is dative because the feeling/state is “happening to” you.

• поэтому = “therefore / so,” it introduces the result:
  Сегодня мне плохо, поэтому я остаюсь дома. = “..., so I’m staying home.”
• потому что = “because,” it introduces the reason:
  Я остаюсь дома, потому что мне плохо. = “I’m staying home because I feel unwell.”

They often pair conceptually:

• потому что → cause
• поэтому → consequence

Yes, typically. поэтому connects two independent parts (two clauses), so you normally write a comma:

• Сегодня мне плохо, поэтому я остаюсь дома.

Russian often uses the present tense to describe a current decision or ongoing situation:

• “Today I feel unwell, so I’m staying home.” (right now / as a plan for today)

It can describe either:

• what is happening now (you are staying home)
• an immediate decision/plan (you will stay home)

• я остаюсь дома (imperfective) = “I’m staying home / I stay home (today)” (process/ongoing/arrangement)
• я останусь дома (perfective) = “I will stay home / I’ll remain at home” (a single decision/result)

In this context both can work, with a slightly different feel:

• остаюсь = more “I’m staying (as my current course of action)”
• останусь = more “I’ll stay (decision / final outcome)”

дома is an adverb meaning “at home.” It’s the most natural choice for “stay home”:

• я остаюсь дома = “I’m staying home.”

в доме means “in the house/building” and sounds more physical/specific:

• я остаюсь в доме = “I’m staying in the house (not going outside).”

No. Word order is flexible, and moving сегодня changes emphasis:

• Сегодня мне плохо... = emphasis on “today”
• Мне сегодня плохо... = emphasis on “to me / my condition,” with “today” added
• Мне плохо сегодня... = “today” can sound more contrastive (“today (as opposed to other days)”)

The meaning stays basically the same.

Yes, often. Russian can drop the subject pronoun when it’s clear:

• Сегодня мне плохо, поэтому остаюсь дома.
  This is common in speech and informal writing.

Keeping я adds emphasis or clarity.

оставаться means “to remain / to stay (behind) / to continue being somewhere.” In everyday Russian it’s a normal way to say “stay home” in the sense of “not going out”:

• остаюсь дома = “I’m staying at home (not going anywhere).”

Another option is сидеть дома (“to sit at home”), which can sound more like “to be home doing nothing / stuck at home,” depending on context.