Machine Learning - Range of Hypothesis space and choiceof Hypothesis function type
I will answer your question as I understand them, the clarity you are looking for comes from the Maths behind ML.


There is no fix range of values of the coefficients or weights. Finding the value of these weights is the work of ML algorithms. although using regularization you can reduce the value of these weights but range depends on algorithm. no. of weights you can decide
Yes, formula is loosely fixed for a ML algorithm. 
e.g. for linear regression in your case

h(w,x) = w0*x0 + w1*x1 + w2*x2 +w3*x3 (where x0 =1)


the weights will change after each iteration though. for neural network it is multiplication of a weight matrix with an input matrix for each layer. 
The output of h(w,x) is the prediction of ML which you can compare against y.


All the ML algorithms available are your hypotheses space(H)


e.g., quadratic, 

linear equation(the one above), 

high degree polynomial, 

complex neural network.