Your questions are interesting, but have they any practical importance?
1) Let's say you are right, then they can't let you go until the 2nd January. Does that matter? Two extra days' pay. You are better off dealing with people on a practical basis rather than trying to get an extra day due to some technicality.
Notice in writing. Again, they have made it clear that they are giving you notice. Maybe in law, you have a right to challenge them on this. If the shoe was on the other foot and you had given in your notice orally, would you feel obliged to stay on another month?
This all gets down to how your employer is handling this. If he is treating you well generally, then you should not be taking advantage of technicalities. If he is treating you unfairly, then maybe take advantage of the technicalities.
2) Again it does not matter. It is not based on whole years. Someone working 5 years and one day, gets a tiny bit more than someone working 5 years.
3) A very interesting question. Leaving out the complexities of the construction industry. If an employee is given two weeks' notice just as they are going on one week's holidays, I would presume that it is a total of two weeks and not three weeks.
You are being paid for your holidays anyway.
Brendan