Very, very small. The biggest risk is in not getting immunized. There are no frivolous vaccines. Unless you have some unique situation the benefit will always be orders of magnitude greater than the risk. Minor soreness and fatigue for a day or so are a small price to pay for preventing the morbidity and mortality of mmr, hep b, etc. Ask anyone post polio. Autism and vaccines has been thoroughly debunked.
SMALL ONES. Generally very mild such as soreness or fever. The risks are far, far, far outweighed by the benefit in preventing the diseases.
Yes. There are risks in vaccines, some more so than others. They are well studied before fda approval and if the risk:benefit ratio is found to be acceptable, it is released on the market. These risks are outlined in vis (vaccine information sheets) which are available from your pedi or online at cdc.Gov. All children should be vaccinated unless there is a specific contraindication. Talk to your doc!