O.K great.
By the sound of that I can offer you several possibilities for each effect.
For the vanish, I can offer you two things:
1)A black art vanish, for which you will need a full background, and some lighting management. For the cover under which you will vanish you can either use a big cloth/foulard, or a good fogger. If you got a few pretty pennies to spend you can buy a nice
flash pot for theatrical effect and some misdirection (if that's the way you are thinking of performing it).
2) A Dekolta chair vanish, if your cousin is a carpenter it would be a walk in the park for him to make one or to "gaff" a normal wooden chain that fits the requirements. For this you will have to buy the plans (cost 30$ and you can sell them on Ebay later, or even give it to your cousin to build more chairs and sell them for a nice profit to magicians) you can find the plans on a lot of magic on-line stores, for example here:
http://www.williamsmagic.com/index.php?main_page=product_info&cPath=41&products_id=11166
To perform it you will need at least one assistant, and again some control over your background.
A fogger or flash pot can also help the effect; all depends on how you want to present it.
For the sawing in half:
1) I strongly suggest Bisection by Andrew Mayne, if you want you can improve it by using his "pocket sawing in half", but then you will have to alter the effect a bit and have an assistant, but you will have a much stronger effect (imagine this: with bisection alone you get to see the bottom half of the "sawed" person, with the combination you can see the upper half on the floor trying to reach the bottom half).
2)If you want to use your cousin's skills to the max, you can build a sawing in half "bed" like the one Penn and Teller used (if you ever got to see them perform it). You can't get plans for it, but if you have a video of them performing it you will understand how to make one right away, and it's not very difficult, only needs a lot of wood.
The only thing good about this method over the first one is that it's a bit more visual, and has the potential to be extremely gory if that's your thing. But I really wouldn't suggest it.