Question in probability- uniform distribution

Question

I am struggling with a question in probability and I'd love to get some help.

It goes like this-

Given an infinite series of independent random variables $X_i$, so that for every natural $i\in \mathbb{N}$ $\,X_i\sim U([0,1])$. We define $Y_i=X_i+X_{i+1}$

and $S_n= Y_1+...+Y_n$

1. Show using the chebyshev inequality that \begin{align*} \lim_{n\rightarrow\infty} \frac{|S_n-n|}{n}=0 \end{align*}

2. Use the chernoff bound to show that for every $a> 0$:

\begin{align*} P(S_n\geq a)\leq e^{-a}(e-1)^{2n} \end{align*}

for 1 I don't understand how can I use they chebyshev inequality to bound the actual expression and not just the probability.

for 2 I am not sure how to calculate the moment generating function (that is required for the chernoff bound) because consecutive $Y_i$ seem to be dependent of one another...

Thank you in advance!