I have the same problem with mine in the kitchen when I turn on the microwave. It was suggested to me to check the wiring connections/ground on the fixture to see if they are loose.
Instead of using a standard light switch, you use a dimmer switch. These can be mounted in the wall like most light switches are or they can be wired into the cord so that only one specific lamp is controlled by the dimmer. Go to Home Depot's web site and in the search window, type "Light Dimmers." You'll find all sorts of them.
Yes. - exactly. For anyone that is unfamiliar with this designation, E12 stands for 12mm diameter. This type of base is most commonly referred to as "Candelabra."
Lutron maintains a page on their website that lists the LED bulbs that have been tested and are certified to work (issue free) with Lutron's LED dimmers. I would recommend that you check this resource prior to purchasing LED bulbs that you intend to dim. Also, this page is updated quite often so make sure you check just prior to purchasing. You may be surprised which bulbs make the list and which ones fail. If you are outfitting an entire house (as in the case of POT lighting), you can possibly avoid costly and time-consuming mistakes.