$1.$ How does BGP prevent loop formation?

$2.$ Consider the following AS graph. Assume Hot Potato is used for intra$-$AS routing, and

AS$\_$PATH length is used for inter$-$AS routing decisions. What will be the path of a

packet traveling from X to Y$?$

$3.$ If we change the weight of the edge between a$3$ and c$1$ from $30$ to $100,$ will the path

from X to Y change? If yes, what will be the alternative path? If not, why?