Heute kaufe ich mein Lieblingsprodukt, weil es im Angebot ist.

German main clauses follow the V2 rule: the finite verb (here kaufe) must be in position 2.
If you put Heute (a time adverb) first, it takes position 1, so the subject ich moves after the verb:

• Heute (1) kaufe (2) ich …

You could also say:

• Ich kaufe heute mein Lieblingsprodukt, weil …
  Both are correct; starting with Heute just emphasizes today.

In German, a subordinate clause introduced by weil is normally separated by a comma from the main clause. This comma is standard in formal and neutral writing:

• … , weil es im Angebot ist.

Because weil introduces a subordinate clause, and in subordinate clauses the finite verb typically goes to the end:

• weil es im Angebot ist

If it were a main clause, you’d have V2 again:

• Es ist im Angebot.

It’s the direct object of kaufen, so it’s in the accusative.
Produkt is neuter (das Produkt), and for neuter singular:

• nominative: mein Produkt
• accusative: mein Produkt

So accusative neuter looks the same as nominative neuter, which is why it stays mein.

German often forms compound nouns. Lieblingsprodukt is:

• Lieblings- (favorite-)
• Produkt (product)

So it’s literally favorite product as a single noun. This is very common in German (e.g., Lieblingsfilm, Lieblingsessen).

Es refers back to mein Lieblingsprodukt (or more generally to das Produkt). Since Produkt is neuter (das), the matching pronoun is es:

• das Produkt → es

Im Angebot means on sale / on special offer.
im is a contraction of in dem:

• in dem Angebot → im Angebot

This contraction is extremely common with in + dem.

No—in Angebot is not correct in standard German. You typically say:

• im Angebot (most common) or sometimes:
• im Sonderangebot (on special offer)

It’s present tense grammatically, but German often uses the present to talk about planned future actions, especially with a time word like heute, morgen, etc. So it can mean:

• I’m buying it today (today’s action, stated simply)

Yes. You can also start with the subordinate clause, but then the main clause still follows V2 word order (the verb comes right after the whole subordinate clause):

• Weil es im Angebot ist, kaufe ich heute mein Lieblingsprodukt.

Notice the comma after the subordinate clause, and kaufe is still the finite verb in position 2 of the main clause.