Yes they'll still get nutrients from the ground, but a little MG S&F wont hurt. You shouldn't need to water more often, but it depends on your soil drainage. I water 2-3 times a week, but I have pretty good soil. I have to dig 18" to 24" to hit clay.

It depends a good bit on what the filling for the bed is as well as the depth. Except for some root crops, most veggies don't have very deep roots that will penetrate down into the base soil if a deep raised bed. But if the bed filler is an enriched mineral based soil (ie. garden/topsoil soil and compost), it might very well supply all the nutrients required for healthy and productive plant growth. OTOH, bagged "raised bed soil" may or may not have a similar compliment of nutes. I agree that some supplemental fertilization will not hurt and quite possibly be beneficial. Even well-prepared inground veggie gardens that are manured or composted annually may need additional nutrient input. Most vegetable crops are heavy feeders and also draw nutrients out of the soil when harvested.

It is impossible to accurately predict the need for more or less watering unless we know the filler soil quality as well as the underlying base soil drainage.