It is hard to imagine anyone using that sentence. Whatever you mean, there is a better way to say it. I'll be studying maths when she arrives.
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JumanahI'll have been studying maths when she comes.When she arrives and you open the door for her, she will be able to say something like, "Oh! I see you have been studying maths." Maybe there will be books, pencils, and papers covered with attempts to solve maths problems on your table.
JumanahThe lesson will have started by the time she arrives.No comma.
JumanahDoes it mean if she arrives, the lesson will have already started?No. There is no "if" in the meaning. The meaning is "when". The lesson will have already sta
JumanahIf I want to say "The lesson will have started, by the time she arrives" Does it mean if she arrives, the lesson will have already started?When she arrives, the lesson will have already started.