That's great to hear that you are feeling more confident
I think it is acceptable to quietly hum something to find your starting note if you are singing without accompaniment, though it's probably better if you can do this before you go in. It might be worth asking your teacher for some tips about finding your note.
I think singing directly to the panel is a matter of personal choice. I would be inclined to pick a spot just over the shoulder of one of them and sing to someone you imagine sitting there. There are two reasons for this 1. If you catch the eye of the panel member - which is likely if you are singing directly to them - you may be put off by a lack of response or a quizzical look and it could throw you and 2. the panel's job is easier if they can observe you without being "observed" back. I find it hard not to be conscious of the audition situation if I look directly at the auditioners and that inevitably leads to a more self-conscious audition. I much prefer not to meet the eye of my auditioners (unless I am talking directly to them in a chat/interview of course

). I find it easier to be in my character's bubble if I can ignore the people assessing my performance.
Very best of luck for Guildhall. I'd love to hear how you get on and what you think of the experience.