Alan

g(f(x))  =  2(f(x))  -  5  =  2(ax + b) - 5  =  2ax + 2b  - 5

Compare coefficients of x with 3x + 4  

so  2a = 3

and 2b - 5 = 4

I'll leave you to complete this.

Yes, the polynomial exists:

Note that the factors of 50 are 1, 2, 5, 10, 25, 50.

x+5 must equal one of these.

The least common multiple of 50 and one of these must be 50.

Can you take it from here? 

Note that the question asks for real numbers - it doesn't restrict the solution to integers.

For cos B change the formula so that A → B, a → b, b → c, c → a

See if you can then work out what to do for cos C.

Use the Cosine rule: \(\cos A = \frac{b^2+c^2-a^2}{2bc}\)

Here:  a = 8, b = 7, c = 5

Cycle a, b and c for the other angles.

Here is one way:

Like this perhaps:

I think the following is what is wanted:

Here are the steps: