You should let your kids use the internet but you have to supervise them. There are a lot of sites just for kids, even browsers for kids, that will give them access to their favorite TV characters. Many are educational too.
The internet can be a useful tool for education. I would not keep them off of it entirely, but I would monitor the information they view and use filters.
Set up parental blockers on the internet. There are many programs that you can get so that they can only access websites that are approriate for their age. Being that they are that young I wouldn't worry too much because you will need to be right there to help them.
Not necessarily. With supervision, they can have an enjoyable learning experience online. There are many good websites, such as pbs. org, designed for children in this age group.