Heute will ich im Kaufhaus eine Jacke anprobieren.

German main clauses follow the verb-second (V2) rule: the finite verb (here will) must be the second element in the sentence.
So if you move Heute to the first position for emphasis, the verb stays second and the subject shifts after it:

• Ich will heute … (neutral)
• Heute will ich … (focus on time)

In this sentence, will means want to / intend to. It is the present tense of wollen (to want).
German usually does not use will to form the future the way English does.

If you wanted a clear future meaning, you would more commonly use:

• Heute werde ich … anprobieren. (with werden
  • infinitive)

But Heute will ich … expresses intention/plan: I want to / I’m planning to … today.

Wollen is a modal verb. Modal verbs combine with another verb in the infinitive:

• Ich will
  • anprobieren = I want to try on

In German main clauses, the modal (will) is conjugated and stays in position 2, while the other verb goes to the end in the infinitive.

With modal verbs (and also with many other structures), German places the infinitive at the end of the clause:

• Heute will ich … anprobieren.

This “verb-at-the-end” pattern is very typical in German whenever another verb (like a modal) is already taking the finite verb position.

Yes, anprobieren is separable: an- + probieren.

• In a simple present main clause without a modal, it splits:
  Ich probiere eine Jacke an.

• With a modal verb, the full infinitive stays together at the end:
  Ich will eine Jacke anprobieren.

So it is separable, but modals keep the infinitive unsplit.

Eine Jacke is accusative because it is the direct object of anprobieren (what you are trying on).

• eine Jacke = feminine accusative (same form as nominative here, but the function is object)

If it were masculine, you’d see the difference more clearly:

• einen Mantel (accusative masculine)

• im is a contraction of in dem:
  im Kaufhaus = in the department store (location)

• ins is a contraction of in das and usually implies motion/direction into:
  ins Kaufhaus = into the department store (going inside)

Here you are describing where you want to try something on (location), so im Kaufhaus fits.

Kaufhaus is neuter: das Kaufhaus.
With in + dative for location, dem is the dative form of das, which contracts to im:

• in dem Kaufhaus → im Kaufhaus

So im Kaufhaus is correct because the noun is neuter and the phrase is dative.

Yes. The difference is mainly politeness/strength:

• Ich will … = strong, direct: I want to …
• Ich möchte … = softer, more polite: I’d like to …

In many everyday situations (especially in shops), möchte often sounds more natural/polite than will.

Common alternatives are:

• Ich will heute im Kaufhaus eine Jacke anprobieren. (very common)
• Ich will im Kaufhaus heute eine Jacke anprobieren. (possible, but usually you’d put time earlier)

German often follows a tendency like time – manner – place, but it’s flexible depending on what you want to emphasize.