[Here](http://fa.its.tudelft.nl/~hart/onderwijs/set_theory/Jech/19-iterated_ultrapowers_and_LU.pdf), on page 358, I would like to know
if the $M$-ultrafilter $U\_i$ on $κ$ is iterable for all $i$'s? 
How do we use and prove this fact? 

And how can I see that $P^M(κ)=P(κ)$ and $M^κ⊂M$?

And finally how can I see that $\{U\_i\}\_{i=1}^{\infty}$ is in $M$?