Definatly, you can but check its PH value and for better absorption it should be in supernant liquid

but will it be cost effective?

Yes, I agreed with Dr.Sakshi about the cost

Cost is major concern for wider adoption is succeeded in pilot study.

Before deciding for foliar application of cashew- apple juice, first one should know the nutrient status/composition of the juice in respect of major and micronutrients. Also one can get information on constituents like aminoacids , organic acids and growth regulators/ stimulants if any. Also see the pH of the juice and the dilution needed before application.Major concern is which use of the juice fetches more income to the farmer/horticulturist. If at all one desires to try this, it is better to study on low nutrient demanding crops like cucurbits or other vegetables.

I think cashew apple is not costly as that of cashew nut. First work out the cost and also analyse the nutrient composition . It it found to be suitable and devoid of toxicity and economic first try it different concentration in pot culture study and decide the concentration

If cashew apple's available in his own farm then it become part of recycling of agril waste or ee can say byproducts. Per tree how much kg apple available, liquid availability decide the solution and further their dilution content decide the overall feasibility.

you can, but it contains some protective material like pigments.

You can use it but it will add to the cost of cultivation.

yes..u can but check Carotenoids content form juice...