Open landing gear significantly changes the plane's steamline and can 'break off' at high enough speeds; although, it may just be military aircraft that reaches that speed. Commercial aircraft are given just enough fuel to make it to their destination...the drag caused by open landing gear may force an emergency fuel. That's why commercial airlines never continue their flight if the landing gear doesn't work properly.

there are aircraft that have a type of landing gear called fixed this means that the can not be retracted to it is possible for a plane to fly with its landing gear out

The landing gear will not "blow off" in the event that they will not retract. There are however speed restrictions due to possible damage to the landing gear doors. Additionally, a large aircraft (corporate jet and up) is designed to be able to take off at a certain gross weight but possibly can not land safely at that same weight. Therefore, the airplane might have to either fly around to burn up fuel or dump fuel if they can to bring the gross weight down to an acceptable weight for landing.

It happens. It increases fuel consumption and decreases speed, so that it cannot proceed with its flight as normal. It will therefore almost certainly return to the takeoff airport, or whichever other nearby airport has the best facilities for fixing the problem. Since aircraft cannot land with the amount of fuel needed for a long flight, thus may involve dumping fuel to lighten the aircraft to a safe landing weight. This in turn may involve flying round in circles for up to half an hour while fuel is dumped before it can return to base. A bore, and a nuisance for all concerned, but no great risk.

In the past few years, the media has tended to make a big spectacle out of this type of event. It all started with Jetblue 292 (google this if unfamiliar) and happened most recently with American 862 in Miami. For most pilots, this is a relative non-event and really isn't that dangerous. Obviously the flight is not going to continue if the landing gear fails to retract or retracts improperly. The first signs of a problem will be a small blinking red light in the cockpit. This light does not tell what the exact nature of the problem is, but warns pilots that something has not retracted correctly. Normally, pilots will then fly by the tower so the controllers can see if there is an actual problem. Once the gear problem is confirmed, arrangements will be made for an "emergency" landing. Sometimes it may be decided that another nearby airport is better suited or has a longer runway/threshold. While this is going on, the plane will probably be in a holding pattern around the airport. In most aircraft, the landing gear is rated to about 170 knots. This is ample airspeed to safely remain in a holding pattern indefinitely. The time of the holding pattern may be extended if the plane is "overweight" for it's upcoming landing. Since the maximum takeoff weight is often drastically different than the maximum landing weight, fuel has to be disposed of. If the plane has the ability to jettison fuel, it will do it at this time. Some smaller planes, like the A320, cannot jettison fuel. In this case, the plane will continue in the holding pattern until enough fuel has been burned off. You don't hear much about these anymore, but if the landing gear is partially retracted, pilots can do a G-force manuever in an attempt to force it back into place. Many times after withstanding the force of maximum airspeed for a while, it will lock back into place. If it doesn't, pilots will elect for either a completely gearless landing or a partially gearless landing. Obviously there will be some risk involved but chances are, it will be fine. One risk includes complete collapse of partially retracted gear causing the plane to spin out of control. This could be accompanied by fire or damage to the plane. Many people fear these incidents because they do not understand the real nature of what is happening. The media makes it sound like a fireball waiting to happen. Sometimes pilots may not be clear about it over the intercom. This leads to fear of the unknown. Rest assured that while this may make people nervous, it is not as big of a deal as its made to be. As an airline pilot, I've dealt with a minimum of three landing gear related incidents in three different planes. All of them were uneventful and didn't cause too much of a headache on the flight deck.