Adding measuruments noises to kalman filter
For the first question, in Kalman filter there are two noises namely process and observation noises. Kalman filter assumes the noise to be Gaussian with zero mean and some variance $\mathcal{N}(0, \sigma^{2})$. Let's say we have a sensor that measures a constant quantity but random, for example distance. Let's say $x = 1$m, however the sensor gives us $z=0.9$m. In reality we don't know $x$ for certain so we rely on our sensor. In Matlab, we can simulate this sensor 

x = 1; % true value
z = x + randn(); % observed value


randn() is normal distribution with zero mean and variance one $\mathcal{N}(0, 1)$. If you want to increase the accuracy of your sensor, then multiply the normal distribution randn() with some small value that you think it is the error of your sensor. 

for i = 1:6
    x = 1; % true value
    z = x + 0.01*randn() % observed value
end


You will notice the observed value varies from the true value however still close to the true value because of 0.01. Remember that Kalman filter is a matter of modeling your system accurately. For kalman filter, you need the motion and observation models given in advanced. Also, your system must be linear and if this is not the case then you should use Extended kalman filter. Moreover, the noise must be Gaussian noise. Now your job to determine these parameters.