Could I land a rasberry pi on the moon for £10,000 or $13,000?

The balloon will get you fairly high, but since the balloon relies on the atmosphere for its lift, it will not reach a height at which true orbit can be maintained. Then you will need to burn a lot of fuel to give the device sufficient tangential velocity to maintain an orbit. After that you will need further fuel to accelerate from the orbital velocity of around 17500 MPH up to close to the escape velocity, which probably requires a speed around 24000 MPH. You will also need to provide enough fuel and rockets to slow the descent on to the moon's surface.

Although the Pi is only a few tens of grams of mass, the fuel tanks, rocket motors and control systems, and of course the batteries to run the Pi, will add many more times the mass of the Pi itself. I doubt whether $13000 would come anywhere close to the fuel bill for the project, never mind the cost of the control systems and the balloon and the fuel tanks.

As the moon is so much smaller than Earth, the "lunar gravity encounter" will be very close to the moon. A fraction of a degree off with the trajectory, and the vehicle is likely to get stuck in lunar orbit, or be thrown back towards the Earth or even sling shot into a trip round the solar system, probably ending up frying in the sun.

The whole vehicle would weigh hundreds or even thousands of kilograms, not the "less than a kg" you seem to think.

No, A balloon does not get you into LEO. It gets you high, but not Orbit you lead escape velocity to do that

Don't be silly, the earth is flat and moon is just a projection.