Í nóvember og desember vil ég drekka meira heitt te og vera meira heima.

Because Icelandic is a verb-second language in main clauses.

The sentence begins with the time expression Í nóvember og desember, so that takes the first position. In a normal main clause, the finite verb must then come second, so vil comes before the subject ég:

• Í nóvember og desember vil ég ...

If you started with the subject instead, you would get:

• Ég vil drekka meira heitt te og vera meira heima í nóvember og desember.

Both are grammatical, but the original version puts extra focus on the time phrase.

Not exactly.

Vil is from vilja, which usually means to want. In many sentences, it can also express intention or something close to English will.

So here vil ég drekka ... can feel like:

• I want to drink ...
• I’m going to drink ...
• I will drink ...

The exact English translation depends on context. Icelandic often uses vilja where English might use either want to or will.

They are in the infinitive form:

• drekka = to drink
• vera = to be

After vil / vilja, Icelandic normally uses an infinitive:

• ég vil drekka = I want to drink
• ég vil vera = I want to be

That is why you do not see a form like drekk or er here.

Because one vil can govern both infinitives when they are joined by og:

• vil ég drekka ... og vera ...

This works just like English:

• I want to drink more hot tea and be at home more.

You could repeat it for emphasis, but normally you do not need to:

• vil ég drekka ... og vil ég vera ...
  This would sound heavier and less natural in a simple sentence like this.

Because te is treated as an uncountable noun here.

• meira te = more tea
• fleiri bollar = more cups

Use meira for more of a substance, amount, or degree.
Use fleiri for more individual countable things.

So:

• meira heitt te = more hot tea
• fleiri tebollar = more tea cups

Because the adjective has to agree with the noun.

Te is neuter singular, so the adjective heitur becomes heitt:

• masculine: heitur
• feminine: heit
• neuter: heitt

So:

• heitt te = hot tea

The adjective matches the gender, number, and case of the noun it describes.

Because these mean different things.

• meira heitt te = more hot tea
  → a larger quantity of hot tea
• heitara te = hotter tea
  → tea with a higher temperature

So the sentence is talking about quantity, not comparison of temperature.

Heima means at home and is an adverb, not a regular noun phrase.

So:

• vera heima = to be at home

In the sentence:

• vera meira heima

this means to be at home more or to stay home more often.

English speakers sometimes expect something more literal like í húsi or á heimili, but Icelandic very often uses heima for this idea.

Here meira does not describe a noun. It modifies the idea of being at home, so it means:

• more at home
• at home more
• home more often

So the two instances of meira in the sentence do different jobs:

• meira heitt te = more tea
• meira heima = at home more

That is very natural in Icelandic.

Í here means in:

• í nóvember = in November
• í desember = in December

As for capitalization: in Icelandic, month names are normally not capitalized unless they begin the sentence. So:

• í nóvember
• í desember

This is different from English, where November and December are always capitalized.

Yes. For example:

• Ég vil drekka meira heitt te og vera meira heima í nóvember og desember.

That is also grammatical. The difference is mostly about focus and style.

• Í nóvember og desember vil ég ...
  puts the time frame first
• Ég vil ... í nóvember og desember
  starts more neutrally with I

So the original version is a very natural way to foreground when this applies.