The course which helped me a lot with understanding many mathematical objects in probability is Intégration, Probabilités et Processus Aléatoires by J.-F. Le Gall (in French, also available in English) . It has a similar structure with Probability with Martingales by D. Williams.
Another frequent reference in advanced probability courses is Probability and Random Processes by G. Grimmett and D. Stirzaker.
As I am not a specialist, for the statistics part, I would refer to the course notes of D. Vyndev.
For the course Stochastic Processes 2, the following could be helpful:
for random walks - An Introduction to Probability Theory and Its Application by W. Feller;
for continuous Markov chains - Markov Chains by J. Norris;
for Brownian motion - Brownian Motion, Martingales and Stochastic Calculus by J.-F. Le Gall.
also, here you can find the problems from the tutorials in 2021 and a mock exam.