I'm also applying for History and frantically preparing for the HAT and I'd actually reccomend that you spend more time on questions a) and b) of part one. Having done a lot of practice I think that they'd be the easiest to get completely wrong if you really misunderstood the source. Don't ignore them just because they are the shortest, you need to really really read the source carefully to answer them well.
With the essays, they may seem more difficult at first but remember there is no set mark scheme and no particular answer that they are looking for, there is more emphasis on writing something interesting and thought provoking that they haven't seen before than just writing them an A level type essay. They know that you can write those, they want to know what else you can do.
Also don't forget the second question, really interrogate the primary source, rip it to shreds if you have to, that's what historians do. I think that this part is the easiest to do well on, just squeeze every drop of information out of it, even if you think an idea doesn't make much sense, if you think that's what the source is saying put it down. They want to original thinking.
Hope this helps and good luck everyone!