Specification of the scream stream cipher is unclear
I've just dived into that paper for you, with the following results:


You've got that one correct.
The eight-byte input is multiplied with matrix M. There is no mention or indication of the polynomial you mention. Simply follow the paper. 

The matrices are fixed [[1,2],[2,1]] and [[1,3],[1,3]]. So, 2 and 3 are NOT replaced by x. The multiplication is on GF(256) with the polynomial specified at page 4. Thus, you have to do something like this: GF256_Multiply(2, S1[x], 0x1C3) where 2 = M1(0,1) = M1(1,0) for example. That's why they call T0 and T1 "lookup tables". These are fixed tables which imply M1 and M2 are fixed too.

(Notice: This was corrected thanks to OP's own research and the corrections OP mentioned in the comments to this answer.)
I think you got a bit confused there. MSB (= Most Significant Bit) and LSB (= Least Significant Bit) define "bits", while the paper explicitly talks about "bytes" in section 3. Therefore, they did not need to define any MSB or LSB. The paper simply defines $byte_0$ (which is, reading from left to right, the leftmost byte), and $byte_3$ (which is the rightmost byte). So you practically extract the 4 bytes into $byte_0$ up to $byte_3$ from left to right (aka "first in, first out").


Hope that helps.