Learn Hardcore Japanese: mise ha mou aite imasu.

は marks the topic: we’re talking “as for the store.” It assumes the store is already in the conversational background or is being contrasted with something else.
Using が—店がもう開いています—is also grammatical and presents “the store is already open” as new, noteworthy info you’ve just noticed or discovered. With は, you might be answering “What about the store?” or contrasting: 郵便局はまだですが、店はもう開いています。

Does 開いています mean “is opening” or “is open”?

It means “is open.” With many intransitive verbs like 開く, the V‑ている form describes the resultant state, not an ongoing action. So 開いています = “it has opened and is (now) open.”
If you truly mean “is in the middle of opening,” you’d describe the action or preparation: 今、開店準備をしています (“They’re getting ready to open”) or, focusing on someone’s action, 今、店を開けているところです (“They’re opening the store right now”).

Why います and not あります?

Here います is the auxiliary that forms V‑ている (progressive/resultant state). This いる is used regardless of whether the subject is animate or not. The いる/ある split only applies to the standalone existence verbs.
Related pattern: V‑てある (with a transitive verb) describes a resultant state due to someone’s intentional action: ドアが開けてあります (“The door has been left open [by someone]”). For “is open,” use the intransitive: ドアが開いています.

What’s the difference between 開いています and 開きました?

開いています = “is open” (current state).
開きました = “(it) opened” (event report; just happened or happened in the past).
For businesses: “has opened (for the day)” is often 開店しました; signs and announcements prefer state-like expressions (営業中です, 営業しています) when they mean “we’re open now.”

How are 開く and 開ける different?

They’re an intransitive/transitive pair.

開く（あく）: something opens (by itself). → 店が開く／開いている (“The store opens / is open.”)
開ける（あける）: someone opens something. → 店を開ける (“[They] open the store.”)
The “store is open” uses the intransitive 開く.

How do I pronounce the sentence?

店 = みせ, topic は is pronounced わ, もう = もう, 開いて = あいて, います = います.
Whole sentence: みせはもうあいています.
Note: 開く can also be read ひらく in other meanings (e.g., “open a book/hold an event”), but for “a store/door is open,” read あく → あいている.

Can I write 空いている instead of 開いている?

They’re both read あいている but mean different things.

開いている: “open” (door/business is not closed).
空いている: “empty/available/not crowded.”
Use 開いている for “The store is open.” Use 空いている for things like seats or crowd levels: 店は空いている = “The store isn’t crowded.”

What’s the difference between もう and まだ?

もう = “already”; with negatives, “no longer.”
まだ = “still”; with negatives, “not yet.”
Examples:
店はもう開いています = It’s already open.
店はまだ開いていません = It’s not open yet.
店はもう開いていません = It’s no longer open (i.e., it’s closed now).
In questions, choose based on expectation: もう開いていますか (“Is it already open?”) vs まだ開いていますか (“Is it still open?”).

Where should I put もう?

The default is before the predicate phrase: 店はもう開いています.
Other orders are possible for emphasis: もう店は開いています or 店がもう開いています. Don’t put もう after the verb.

Is it okay to add よ, ね, or make it a question?

Yes:

店はもう開いていますよ: informing/assuring.
店はもう開いていますね: seeking agreement/softening.
店はもう開いていますか: “Is the store already open?”

Are spaces normal in Japanese writing?

No. Learner materials sometimes add spaces for readability. The natural way is: 店はもう開いています。

How do I say this more casually or more formally?

Casual: 店、もう開いてる。 / もう店やってる。
Polite (as given): 店はもう開いています。
Extra-polite/business: 店はもう開いております。 or better: ただいま営業しております。
Common signs: 営業中 (open), 準備中 (preparing), 閉店 (closed for the day), 臨時休業 (temporarily closed).

Can I use 営業しています or やっている instead of 開いている?

Yes.

営業しています is businesslike/formal: “We’re operating.”
やっている is very common casual speech for “open/operating.”
Avoid 開店しています; say 開店しました (“has opened”) or 開店中です (“open for business now”).

Why is は pronounced “wa”?

When は is the topic particle, it’s pronounced わ. The spelling reflects historical sound changes; inside words it’s read は (ha), but as a topic marker it’s わ.

Do I ever add です after 開いています?

No. 開いています already uses the polite auxiliary います. You don’t add です after a verb phrase like this. You can add sentence-final particles (よ/ね/か), but not です.

How do I say the opposite?

Polite: 店はもう開いていません。 or 店は閉まっています。
Casual: 店、もう開いてない。 or 店、閉まってる。