Sobald du nach Hause kommst, ruf mich bitte an.

Because Sobald du nach Hause kommst is a subordinate clause (introduced by sobald). In German, subordinate clauses are usually separated from the main clause with a comma:

• Sobald
  • clause, ,
    • main clause
      So the comma is required here.

After subordinating conjunctions like sobald, German uses verb-final word order in that clause. That’s why kommst goes to the end of the subordinate clause:

• du (subject) + other info + kommst (finite verb at the end)

In the main clause, the verb is normally in position 2—but here it’s an imperative (a command), and imperatives typically start with the verb:

• Ruf mich bitte an.
  So it’s normal (and expected) for the verb to come first in commands.

Both exist, but ruf is the common spoken/written imperative for du in everyday German. Rufe is possible but sounds more formal or old-fashioned in many contexts.

Imperative forms (du):

• anrufen → ruf ... an (common) / rufe ... an (less common)

Because anrufen is a separable verb (an- + rufen). In main clauses (including imperatives), the prefix often goes to the end:

• Ruf mich bitte an.

But in subordinate clauses, it stays attached:

• ..., weil du mich bitte anrufst.

Anrufen takes the accusative object (who you call). So I call him/her/me uses:

• ich rufe ihn/sie/mich an (accusative)

Mir (dative) would be used with verbs that take a dative object (not the case here).

They mean different things grammatically:

• nach Hause = direction/movement (going/coming home)
• zu Hause = location (at home)

Since kommen involves movement toward home, nach Hause is the natural choice.

German often uses the present tense to talk about the future, especially when the time is clear from context (here, sobald makes it future-oriented):

• Sobald du ... kommst = as soon as you (will) come home

Using werden isn’t necessary in this type of sentence.

Yes, that’s completely natural. If the main clause comes first, you still use a comma before the subordinate clause:

• Ruf mich bitte an, sobald du nach Hause kommst.

Word order inside the subordinate clause stays verb-final.

Bitte softens the command and makes it more polite—similar to adding please. It’s optional grammatically, but it changes the tone:

• Ruf mich an. = more direct
• Ruf mich bitte an. = friendlier/politer

Yes, du makes it informal (used with friends, family, kids, etc.). A formal version uses Sie and the corresponding verb forms:

• Sobald Sie nach Hause kommen, rufen Sie mich bitte an.

(Notice: kommen and rufen match Sie.)