this expression can be used instead of "in the meantime"??
Generally, no (at least in U.S. English). Meanwhile and meantime can each be used as a noun or as an adverb, so I can understand why they seem interchangeable. I rarely see "meanwhile" used as a noun, however. But this question has nothing to do with the phrase being grammatically correct or not.
Instead it is because meanwhile isn't used that way in everyday communication, and sounds strange to a native speaker. If you were in some region where in the meanwhile were the preferred phrase, you would want to always say that instead of in the meantime. But a region like that would be unusual, according to an ngram search:
At the beginning of a sentence (based on capitalization):
In the meantime
In the meanwhile
After the beginning of a sentence (based on capitalization):
in the meantime
in the meanwhile
If the ""in the meanwhile/ meantime" use in the initial of a sentence, the punctuation of "," should be used immediately after that? what about in the middle of a sentence?
It will depend on how the phrases are used, and how formally correct you need to be, but the answer is probably "yes, you should follow the phrase with a comma".
If you are using one of these as a preposition, which is a common case in which the phrase would be at the beginning of a sentence, using a comma is appropriate but will probably not cause you problems if you do not use one:
In the meantime, you can read a magazine.
In the meantime you can read a magazine.
If you're using the phrase as an appositive, a comma is definitely going to be expected:
Your car will be fixed in an hour but, in the meantime, you can read one of our magazines.
Similar to the preposition, you will probably not have problems if you leave the comma after the phrase out, but the appositive is demonstrated more clearly in writing with the comma included.
what formal expression can be used instead of them?
I'm not sure how formal an expression you want, but any expression which indicates that
- Some amount of time will need to pass until some event, and
- That something else can be done until that event
will be fine. Some options might include:
While you're waiting
Until [time or event] (like, "until then" or "until dinner is ready")