is it possible remove cart or how to solve my issue?

hi
i have some product in my site and i want these low in selling that:
1-each product can't buy more than 1 time.(i use limitation value forever is 1 and it is ok and set quantity per order to 1)
2-i don't want any cart system or basket. i want simply customer can buy product without cart system because maybe sometime one customer go to middle of buy steps and want exit my page. and then come back to buy that but beacause i remove any cart menu and module, he can not do anything to remove product that is exist in his cart from previous discontinue buy steps. and he give error that you can add more to your cart.
is there any suggestion to solve this?
my problem in brief: i don't want use cart to add product, also each product can buy only one time for each user forever. in this way if he add product to his cart via incomplete steps,how can remove that? or how can bypass cart?or each you say...