Hello.

I know there's no difference between "if" and "whether". But sometimes I forget the right usage of verbs after conjunctions. Are these sentences correct?

I wonder whether/if she replied me

I wonder whether/if you're at school

I wonder whether/if he'll be here today

I wonder whether/if you've been done your hometask.

I wonder whether/if you could kill my cat.

Is there any distinction between whether/if "he will" and "he would" ?

Thanks.
Either can be used in your examples (though they need other correction).
Thank you! Could you correct it, please?
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I wonder whether/if she replied to ...

I wonder whether/if you've done your hometask (homework)

Is there any distinction between whether/if "he will" and "he would" ? Yes, definitely.
I have underlined the problem areas:

I wonder whether/if she replied me

I wonder whether/if you've been done your hometask.
well, thank you both! I understood my mistakes except for one issue. On the other web site my first sentence was fixed to "if she had replied to me". Do we really need to use "had" only?
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The information you are supplying is incomplete, fattyshank. Unless there is extraordinary content which I cannot imagine offhand, your options are these:

I wonder whether/if she replied to me

I wondered whether/if she had replied to me
thank you!