Hello!
With respect to your three queries, I'm not too familiar with the first, because I didn't do any MUEP extension units, and the people in the ScSchProg. in my year level didn't credit their units, I think. I remember during Orientation though, that the course coordinator said it was possible (anyway, I think when you originally submit your units, you will have one of the course coordinators with you, so you can talk about prior unit credit then, if not, it'll definitely be somewhere during the enrolment process).
It is possible to do a 2nd year subject (technically, it's a 2nd-level subject) in 1st year. DisaFear is correct in stating that MTH2010(or MTH2015) can be taken in second semester if you do MTH1030/1035 in 1st semester. It's also possible to do MTH2032 (Differential Equations) or MTH2021 (Linear Algebra) after having done MTH1030. (I know two or three people who did MTH2032 in their 2nd semester of 1st year, and two who were doing MTH2021 in their second semester).
If you did MUEP Maths (MTH1040), it may also be possible to do the second-year maths unit Real Analysis (which runs in 1st semester), which another guy did. In terms of difficulty, I've only experienced MTH2015 (and therefore MTH2010, as the lectures are shared). To me, difficulty of MTH2010 didn't seem to really increase compared to MTH1030. I haven't heard from the guys who did MTH2032 or MTH2021. The guy who did MUEP Maths told me he just managed to HD Real Analysis, so doing a 2nd year maths unit straight up is certainly no mean feat.
With regard to the acceleration of your course, in my humble opinion, it's probably better that you don't. You've stated you would like to do Honours and a Ph.D, a choice I have great respect for. In order to do Honours, it's necessary to have 4 3rd year units in relevant units (3 of which must be related to the area you wish to do Honours in) and it's a really really good idea to get good scores in Uni, so that you have a chance at getting Honours scholarships (moreover, you need at least a Distinction average in those units to qualify, scholarship or no scholarship). To me, it just seems like an increased difficulty to be doing higher-level units in your earlier years at uni (just my two cents' worth).
why not both?
2nd year subjects usually build on 1st year subjects. that sounds like a prestigious program so you could try asking for permission to skip to second year subjects if you have self studied the prerequisites. why do you want to complete it in two years anyway? like DisaFear, i intend on prolonging my stay at uni for as long as possible lol
There are forms that you can fill in to take a unit without its prerequisite(s), but you'll need the permission of the unit coordinator in the end.
Anyways, if you do end up joining the scholar program, I hope to see you at Monash next year!
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