Listing first 8 bits generated by LFSR
A few things have gone wrong:

You've reversed the initial state, but continued to shift from left to right. If you do reverse then the shift is from right to left.
You've confused the output bit (the oldest bit in the register) with the feedback bit (the new value that is introduced after shifting)
The feedback rule for the polynomial $x^4+x^3+1$ is $s_{i+4}=s_{i+3}\oplus s_{i}$ and so in your notation would be $s_4$ xor $s_1$

With this borne in mind the first two rows of you table should read as follows:
s1  s2  s3  s4  feedback bit (s4 xor s1)  output bit (s1)
1   0   1   1   0                         1
0   1   1   0   0                         0...

and so on