How much force should be applied in a car to allow it to climb a wall? I know this is a weird subject to talk about, but don't mind too much about specific numbers.

*

*Let's just say that this vehicle has a mass of your choice (a normal
car, for example) and has a turbine on its back, like M35 Mako from
Mass Effect.

*This turbine (which you can exclude weight, fuel etc)
is able to redirect its direction.

To climb this wall, the energy required to keep this car on the wall, so the wheels can have more traction, and thus, be able to climb it, should be at least strong enough to lift the car itself?
The direction of the thrust is also important? It should be thrusting downward (so, lifting the car), or in the direction of the wall, so the tires are able to have a better grip on its surface? Or both?
 A: 
It should be thrusting downward...? or in the direction of the wall...? Or both?

That depends entirely on you. You are the author of the puzzle. As others have pointed out in comments, if the tubojet is pointed downward, and if its thrust exceeds the weight of the vehicle, then you don't need the wall (or the car's engine) at all. The turbojet alone can lift the car.
If you choose to point the jet horizontally, so that it only presses the car's wheels against the wall, then you need to meet two conditions for the car to be able to climb:

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*The car's regular engine must be able to generate enough torque at the wheels to lift the weight of the car, and


*The jet engine must press the wheels firmly enough against the wall that the static friction between wheels and wall can hold the weight of the car.
In order to know how much thrust the jet must make in this case, you need to know the coefficient of friction between the rubber tires and whatever it is that the wall is made of. The greater the coefficient, the less hard the jet needs to thrust.

According to my sources, the coefficient of friction between rubber tires and a concrete surface is somewhere in the neighborhood of 1.0. If that were true, then the thrust provided by the jet would have to be the same as the weight of the car.
The most economical answer in that case would be to point the jet straight down, and not use the car's regular engine at all.
If the coefficient of friction were greater than 1.0, then you could maybe find a more economical solution using less thrust, at a different angle, but I'll leave that as an exercise for the reader.
A: You have three options. One is to have a jet engine that propels the car directly. The second is to have a jet engine that is used only to press the car against the surface of the wall so that the car's engine can propel it via the driving wheels. The third is to combine the other two in a hybrid.
The choice of option depends upon the relative power of the jet and the car's engine, and on the coefficient of friction between the tyres and the surface of the wall.
Accelerating vertically upwards requires a thrust of more than 1g. Most cars don't accelerate at 1g `(which equates to a 0-60mph time of under 3 seconds), so an average car wouldn't be able to accelerate up a wall even if there was enough friction.
You would need to generate enough friction to support the weight of the car. With a very rough wall and grippy tyres, you might get away with a horizontal thrust equal to the weight of the car; but if the wall was smooth, then you would need much more horizontal thrust, in which case you would be better off just directing the jet downwards and propelling the car that way.
If you adopt the hybrid, you redirect some of the jet's thrust horizontally- whether that is worthwhile depends upon whether the loss of upward thrust is offset by the extra thrust you get from the car's engine, which in turn depends on the coefficient of friction between the tyres and the wall and the engine's power.
A: Do not use the turbine to press the car to the wall - use it to suck the car to the wall.
The turbine can additionally be angled upward from the roof (pressing the car down on the driving-surface), or backwards (pushing the car to wherever the car is pointing).
Of real interest in this scheme is where the turbine is getting the air. If the cars underside is properly designed(*), the underpressure created below it will act so the delta relative to atmoshperic pressure, multiplied with the cars area, works to hold the car on the surface. For instance on earth, every square meter can generate 10 tons of force (100 000 N) if there is pure vacuum below the car... which is unrealistic. But with a turbine equipped car weighing about 3 tons, and the turbine sucking just .05 atmosphere, a 4x2m car will be very comfortably sucked to the wall (or ceiling, for that matter).
(*) It might need a skirt
