mmm i can't really say whether science or biomed is better and ultimately if you want to work as a lawyer it doesn't matter which you choose (subject to one minor qualification that I will list below).
I don't know that much about biomed but my perception is that it is harder than science. From people I know doing biomed they often say there is a ridiculous amount of material to learn and a lot of rote learning. If you are just interested in the academic side of biomed, consider that you can do science majors that pretty much cover the same material (molecular biology, biochem, genetics, microbiology etc). I think the only thing you can't do in these science majors which you do in biomed is cut up cadavers

so to answer first question, science i think is easier. I don't think it matters what you take in the long term. If you want a lab job either science or biomed can get you there. If you want a law job, then your non-law degree doesn't really matter (I mean I know performing arts/law people who work at Mallesons).
There is one small issue however which i alluded to above. A few of specialist intellectual property and patent firms require a major in chemistry or chemical engineering. I haven't really researched this much but there may be a way around it but just something for you to keep in mind. Also specialist patent firms aren't really as 'law' related as you may think. If you look up the profiles of the partners at such firms (Davies Collison Cave, Griffith Hack) a lot of them come from science backgrounds. Many of them have PhD's and quite a few don't even have law degrees. Also these aren't really firms you can start working in once you graduate. You will most likely want to start at a more 'general' law firm rather than a specialist firm.
i have not much clue about work conditions as a patent lawyers. I have been told by lawyers that intellectual property is a very niche area of law and isn't really something most people specialise in. Often you work in a range of different areas.
No idea about medico law...
How to do well in first year law... umm, first don't put off your court report assignment to the last day! Don't think you'll just rock up to Court and see a nice case to write on, you'll either walk into some month long murder case or a 10 second traffic offense case. I recommend going to the Magistrates Court and sitting in on a civil hearing (The clerk will probably tell you to go to the criminal courts but unless endless traffic offences is your thing I'd suggest you hear a civil case, usually better to write on - not just because they are longer but because the essay topic is usually about access to justice or something and a lot of people are self-represented in these simple civil matters because legal aid doesn't cover civil cases - instant discussion point right there).
If you're doing contracts then really just stay up to date and do heaps of practice problems such as the ones you get in your tutorials. It's one thing to know the law and another to be able tow rite an answer under time pressure and law exams are usually a massive race against the clock.
Are there things I should be doing now for my career in the future? (eg. Prizes, competitions, work experience)
basically do what ninwa said

It can be quite hard getting a legal related job in first year because most first years only really have retail experience or something similar. Try to work your way up to these types of jobs though. That might mean starting with something like reception or basic office jobs (filing letters, photocopying stuff, coffee boy) and moving up from there. Volunteering at community legal centres is a good way to get law related work experience but they are very competitive to get in to. Try not to overcommit too much with work because you don't want it to hurt your grades so much and it is very easy to take too much on in your first year of uni.
for first year do all the competitions you can and ideally win as many as you can

The moots are probably the most important but also the most stressful and time consuming. If you can spare the time, do the general moot at the start of the year. This is basically the open moot where you will be up against 3rd years so you will probably get slaughtered but the important thing is to experience what mooting is like. Then once first year moot rolls around you will have a tremendous advantage over everyone else because while every one else has no idea what is going on you will probably be far more confident. The teams that win the first year moot tend to have also participated in the general moot as well.
Also socialising is important. make sure you get to know people in the LSS because you will be dealing with them a lot and it helps down the track if you want to apply for LSS positions. Also it helps to now people in the year above you because its a constant source of notes, advice and books

There is really nothing you need to study now. If you are totally bored i guess you can start reading the Laying Down the Law textbook but it is very dry and just to give you some basis of the Australian legal system (which you'll cover in lectures anyway).