If not is negating a finite verb, i.e. one that is connected to and inflected by a subject, then not should come after a helping verb, meaning verb to be, modals and auxiliary verbs be, do and have, for example:
I am not well today.
I have not finished my assignment yet.
Don't you have better things to do?
She was not paying attention.
This is what is normally called negative clause
However, if the verb being negated is nonfinite, which means infinitives with and without to, participles, except for perfect tenses, and -ing gerunds, except for progressive tenses, then not normally comes before the verb it negates:
It is common not to tip severs in some parts of Europe.
The problem was solved by not using the defective part in further projects.
"The Road Not Taken" is a poem by Robert Frost.
I can think of a hundred reasons not to come.
Likewise, it is possible to negate words and phrases other than verbs, normally by placing not right before the word or phrase one wishes to negate. Your first example falls into this category.
Perhaps not surprisingly, he was cautious about committing himself.
He won not only the championship, but also the hearts of thousands of fans.
Yes, you can – but usually not as you put it. There's a pertinent explanation in Swan's Practical English Usage (260.1):
We use will with if to talk about what will happen because of possible future actions – to mean ‘if this will be the later result’. Compare:
We'll go home now if you get the car. (condition)
We'll go home now if it will make you feel better. (result)
So no one would say this:
I will appreciate it if you will send me my bag.
because you're essentially saying that you'd be happy to show gratitude if that will make them send you your bag, as though there'd previously been an argument between you and the other person who said:
I'm not sending you your bag if you don't thank me beforehand!
However, your sentence would never be interpreted as such – outside the bizarre context I made up above, and even then it would be rephrased into something like
I'll say "thanks" if that'll make you hand it over.
which is still weird but less weird than the original – but rather as a non-native English speaker's attempt to say what BillJ said in their comment (a closing quotation mark added):
"I would appreciate it if you would send me my bag" would be the usual polite phrasing. "I would" can be reduced to "I'd" in informal contexts.
Best Answer
There's no rule against using the same auxiliary verb, including will, more than once in a sentence.
Consider these two examples, written by native speakers, found in a search for "will decide that he will":
(source)
and
(source)
In fact, you could have used it three times by using will before come, but it's probably better to avoid that much repetition.
So there is nothing wrong with your sentence grammatically.
You could use the simple present instead of the first future will, as in
but without a context that makes it clear that you are talking about the future, using future will seems better; by using future will in your sentence it is much clearer that you are talking about future time.
I call will in your sentence future will because the modal verb will has other uses than to talk about future time.