First off, congratulations, you are making mead (and yes, if you add fruit it is a melomel). Unless you like really dry wines you made a good choice getting the extra honey. Without knowing the type of yeast that they used in the kit it is impossible to give you specifics but here are some thoughts. First, mead is more like wine than beer. In other words a 1 week primary, 2 weeks secondary, 3 weeks in bottle isn't going to cut it.
Let your mead tell you when it is done with primary fermentation. When it gets to 1 to 2 bubbles a minute in your airlock you know you are close. Transfer it to a secondary container to get it off the yeast trub and then add the puree (and pectic enzymes if you choose). You do not have to add the second package of yeast. In fact, I probably wouldn't. Take a hydrometer reading and see what it is. If is above 1.035 or so I would add the yeast, otherwise I wouldn't worry.
Yes, fermentation will probably restart when you add the fruit but that is no problem (that is what yeasts do). The fruit will not add that much sugar to the mead so don't worry about it making it too sweet. Let it sit on the puree for at least two weeks before transfering it off the fruit to age.
Ideally you want to let your mead age for a year before bottling (take gravity readings and if there is no change over a month or two you can bottle). Check it about every 3 months and if it throws lees then transfer it again. If not, let it sit. I know that seems like forever but it will be worth the wait.
Good luck, let us know if you have any further questions.
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