Secret Sharing between $x$ parties
So for an unknown number of parties $x$, I make $x-1$ random $n$-bit strings represented by {$r_1, r_2,...,r_{x-1}$}. Where  $s$ is the complete string split up between $x$ parties (yes?). 
  
  I then send each party one of the fragments $s_i$, so party 1 would get $s_1$, party 2 would get $s_2$ etc. all the way through to $s_{x-1}$. Along with these fragments. I then send $r_1⊕...⊕r_{x-1}⊕s$ to party $x$.


That is not how it is typically done.  One issue is that two parties (say, party 1 and party $x$) get partial information of the shared secret, that is, the part that was masked by $r_1$.

Instead, what we do is make $x-1$ random strings (each as long as the secret $s$).  Then, we send party 1 the string $r_1$ (not $s_1$), party 2 would get $r_2$, etc.  And then send $r_1 \oplus r_2 \oplus ... \oplus r_{x-1} \oplus s$ to party $x$.

This can be seen to yield no information about $s$ to any $x-1$ parties, and still makes $s$ recoverable to someone with all $x$ shares.

Studying this version of the protocol may answer your questions.