Esik, mégsem maradunk otthon.

Here esik means it is raining.

It comes from the verb esni, whose basic meaning is to fall. In weather expressions, Hungarian uses it for rain:

• Esik. = It’s raining.
• A hó esik. = Snow is falling.

So in this sentence, Esik is a very natural short way to say It’s raining.

Hungarian does not use a dummy subject like English it in weather expressions.

In English, you have to say:

• It is raining.

But in Hungarian, you simply say:

• Esik.

There is no separate word standing for it. The verb alone is enough.

Mégsem means something like:

• yet
• nevertheless
• even so
• still ... not

In this sentence, it shows a contrast between expectation and reality:

• It’s raining, but even so we are not staying home.

So mégsem often suggests: you might expect one thing, but the opposite happens.

Good question. Both can introduce contrast, but mégsem is a bit more specific.

• de = but
• mégsem = and yet / even so / nevertheless

Compare:

• Esik, de nem maradunk otthon.
  = It’s raining, but we’re not staying home.

• Esik, mégsem maradunk otthon.
  = It’s raining, yet we’re not staying home.

The version with mégsem sounds more like despite that fact, so it carries a stronger sense of unexpected contrast.

Maradunk means we stay or we remain.

It comes from the verb marad = to stay / remain, and the ending -unk shows we.

So:

• maradok = I stay
• maradsz = you stay
• marad = he/she/it stays
• maradunk = we stay

In this sentence, maradunk otthon means we stay home.

Because Hungarian verbs usually already show the subject.

In maradunk, the ending -unk tells you that the subject is we, so mi is not necessary.

• Maradunk otthon. = We’re staying home.

You could say Mi maradunk otthon, but that adds emphasis, like:

• We are staying home.

Without emphasis, Hungarian normally leaves the pronoun out.

Otthon means at home or home, depending on the sentence.

In maradunk otthon, it means stay at home / stay home.

This is a very common expression:

• otthon marad = stay home

So the whole second clause means:

• we are not staying home

Because otthon is already an adverb-like word meaning at home.

Hungarian often uses it directly with verbs of staying or being:

• Otthon vagyok. = I am at home.
• Otthon maradunk. = We are staying home.

So you do not need an extra ending here.

It is present tense.

However, like English present forms, it can sometimes refer to a current situation or a near-future plan, depending on context.

So mégsem maradunk otthon could mean:

• we aren’t staying home
• we won’t stay home after all

The exact English translation depends on the situation.

The comma separates two clauses:

• Esik = It’s raining.
• mégsem maradunk otthon = yet we’re not staying home.

Hungarian normally uses a comma before conjunction-like contrast words linking clauses, especially when two full statements are joined.

Yes, but not because Hungarian has only one possible order. It is more about what sounds natural and what is being emphasized.

This order is very natural:

• Esik, mégsem maradunk otthon.

First you state the fact, then you give the unexpected result.

You could also hear:

• Esik, de mégsem maradunk otthon.

That is also natural, with de added for extra contrast.

But the original sentence is already complete and idiomatic.

Yes. Since esni basically means to fall, esik can have other meanings in other contexts.

For example:

• A hó esik. = The snow is falling.
• Leesik. = It falls down.
• Jól esik. = It feels good / is enjoyable

But when esik appears by itself in a weather context, it normally means it’s raining.

It is perfectly normal everyday Hungarian.

Nothing in it is unusually formal, literary, or old-fashioned. A native speaker could naturally say this in conversation.

The word mégsem is common and useful, especially when you want to express despite that or after all, not.