I don't think it's possible to transfer into dalyell scholars during your degree, it's atar-based and offered to high achieving school leavers so it's something you're invited into during enrolment. it's often dropped by people bcz dalyell is not a very helpful thing unless you want to study abroad for free during the degree (I could be wrong) and dalyell units are kinda annoying to do. employers don't care about it either
as for the difference in BSc and BSc (advanced) it's simply the bigger research aspect in the latter. advanced has additional units you can take that are again research-related and you get to do an independent research project. it's good because if you want to then do honours in 4th year (research year) you already have a fair bit of research experience or foundation. otherwise BSc and BSc (advanced) are similar in terms of degree structure and coursework, you still get to complete major(s)/a minor, do electives etc.
also im guessing you're referring to usyd