Using the digits 1, 2, 3 & 4 each once only, and as many +, -, x, / and brackets as you need, try to make as many different numbers as you can, starting at 0, 1, 2 ....

Which is the first number that you cannot make?
My answer is 3.

Which is the largest number you can make?
My answer is 36.

How many different ways can you make 10?
My answer is 3.

Please can you check the following:

(3+2)-4-1=0
(1+4)-3-2=0
(2-1)x(4-3)=1
(4-3)+2-1=2
(4x2)-3-1=4
(4x2)x1-3=5
(4/1)/2x3=6
(4+3)+2-1=8
(4x3)-2-1=9
(3+2)+4+1=10
(4x2)+3-1=10
(1+4)+3+2=10
(4x2)+3+1=12
(2+1)x3+4=13
(4x3)x2+1=25
(2x3)x4+1=25
(1+2)x3x4=36
(2+1)x3x4=36

I have been unable to make 3, 7 & 11.

You missed a bunch, such as

(2x3)x(4+1) = 30
(2+3)x(4x1) =24
(1+2)x(4/3)=4
(1/2)x(4+3) = 7/2
(1/4)x(3/5) = 5/12
(1/3)-(2x4) = 8/3
(1/4)+2+3 = 21/4
(1+4)/(2+3) = 1 ,

but your answers to the three questions appears correct.