I installed a ceramic cooktop (electric of course) which required a sort of shield to be constructed underneath. This wasn't really for radiant heat protection as such, but to stop stuff in the drawers/cupboard underneath from touching the bottom of the cooktop which gets pretty hot. Maybe look at the requirements for gas cooktop installation, and go for it. Otherwise as RavingMad says.
Sure. You might have to cap off a line or two that used to lead to the stove, and possibly reconfigure the gas inlet a tad, but there's no reason why you couldn't reuse the burners in a cook top configuration with a little bit of creative plumbing.
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Maybe look at the requirements for gas cooktop installation, and go for it.
Otherwise as RavingMad says.