Both of these sentences are grammatically correct although there is slight difference: "我必须今天去购物" emphasizes "today". "我今天必须去购物" emphasizes "shopping". "购物" can mean both food and other goods, just like the English word "shopping". : )

There is no grammar mistake, but you should figure out which u wanna emphasize. It depends on the situation you faced. If you have not shopping a couple of weeks or mouths, you wanna emphasize "must".. The sentence should be 我今天必须去购物. You wanna emphasize "must". If you won't have any other time after today, you wanna emphasize"today"-----我必须今天去购物 So put 必须 before the the part you wanna emphasize. And also remember accentuating the emphasized part in speaking.

yes, it is.

It can mean everything you want to buy.

Can this mean food, or is it other goods?