Is it possible to make an electromagnetic shield? Is it possible to make an electromagnetic shield to protect something (or ourselves) against things like bullets, human attacks, metals thrown on us or simple dust particles to protect  a spaceship travelling at high speeds?
 A: Well, in a sense any kind of hard surface is an electromagnetic shield.  Why?  Because the forces holding atoms together and pushing them apart are electromagnetic.  For example, the reason you don't fall through the floor is because the atoms in the floor electrically repel the atoms in your shoes.  This is an electromagnetic interaction!
If you mean a shield to redirect projectiles before they hit us, that would only be possible if the projectiles have a net electric charge.  In that case, a magnetic field would do nicely since the force on the projectile would always be perpendicular to its velocity.  In fact, that's how Earth's magnetic field protects us from the solar wind.
A: 
Is it possible to make an electromagnetic shield to protect something
  (or ourselves) against everything which is attacking?

It is possible to shield very well against some types of electromagnetic radiation. For example, putting a cell phone inside a "Faraday bag" will block enough radio waves from reaching the cell phone that it can not receive incoming calls.
It is not possible to shield something "against everything".
A: In nuclear fusion power plants, electromagnetic fields might be used to contain plasma. But I am not sure what would happen if you threw a solid at the electromagnetic field.
A: sort of, Defense/tech firms are working on plasma integrated projectors, high level magnetically cohesive devices to contain them. They exist by our tech standards...
NASA is working with private research to make a plasma projection screen, that'll disentigrate particles before they impact. However small particles.... (0.01-1 mm)
will Energy shields as we see in Scifi exist, probably not in the classical sense.... Namely the energy demands and thermal properties make them impractical, dangerous.

Being hypothetical… an Arleigh burke Destroyer is 529 feet long, 66 feet wide, 105 feet high (at mast) So has a prism volume at sea level occupying 3.6 million cubic feet (not including hull underwater)

To protect it with a “shield” envelope. A Bubble dome encompassing the ship… Would have a surface area just shy of 444,000 Square feet, A perfect sphere in half, not including below water level.....
On the other hand; the surface area of the ship if you want some kind of "Hull contour" hugging shield

In any Case...Generating sufficient energy to make a plasma is obstacle number one.
Obstacle 2 is Feedstock for the plasma....
Electrons need a specific amount of energy in order to overcome their barrier of outermost electron shells...since plasma is a loose association gaseous matter with free elections. Inert gases like Helium or neon, etc.

Getting back to energy consumption....translates to a minimum energy of 482.43 Mole to highest of 2.413 MJ/mole or about 482.43 kJ/mole to 2.413 MJ/mole.   Thats 375.5 Kilojoules per kilogram or as high as 593.5 Megajoules per kilogram depending on gas used. The average density of the lightning plasma is 0.129 kg per cubic meter... So a bubble shield with area of 444,000 sq ft or 41,248 sq meters with a thickness just a centimeter thick gives you a plasma volume of 412.5 cubic meters. and if similar density mentioned above.... a mass of ~54 kilograms. Energy must be constantly expended to maintain this plasma, at normal atmospheric pressure. Even at a minimum of 375.5 kJ/kg per second, In reality even a high energy plasma is insufficient to stop a projectile. To say nothing of How much energy needed to maintain a magnetic field.
A 50 caliber bullet (12.7x99mm) has a kinetic energy of 18 kilojoules, and delivered over a surface area smaller than a dime...A shield would need 18 kilojoules per square centimeter, to stop the bullets impact needs solidarity to stop it so needs greater than 18 kilojoules per square centimeter, with a bubbles surface area of 412 million sq/cm needs nearly 7.5 Gigajoules to maintain a shield energy of surface area of the bubble....EVERY SECOND, or 7.5 Gigawatts of consecutive power. The Kori Nuclear plant in Busan, South Korea produces 7.5 GW.

Oerliken's 35x228mm Cartridge has a kinetic energy exceeding 380 Kilojoules.

Would need a shield bubble exceeding 156.6 Terajoules.
Heat dissipation: Energy of that magnitude, not to mention generating a plasma bubble, can generate temperatures as high as 10-20 thousand degrees Kelvin. Temps in a confined bubble would have to be dissipated or expended or risk heat enveloping habitable volume of the ship; ionizing airs oxygen into toxic ozone and just plain needing a chilling/cooling system to keep the crew from roasting in an all metal container.
EM visibiltiy: A shield capable of blocking directed energy like lasers.... would have to block visible light, meaning seeing outside the bubble would be impossible. Beyond that blocking EM radiation, means all sensors that use the same EM radiation would be unable to work in the confines of the shield bubble.
