for Q1, there's no reason not to include (2,2) as well (twice)
for Q3, three events would be independent if p(A and B and C) = p(A)p(B)p(C), and the three possible pairs are independent (e.g A and C), just a natural extension from two events
ok, finding probabilities means integrating the probability density - P=|\Psi(x,t)^2| - over parts of the box
try integrating over the whole box first, what does this give you?...
I think Sussex has a fairly strong Physics department, though most employers I suppose would just consider general science reputation, or overall "ranking".
The big cut-off in employability does come between a 2:1 and a 2:2, you only have to look at most typical large graduate employers...
I think at undergrad level it's really difficult to think of a topic entirely by yourself, especially as you say college is starting to drag. Do you have any computational physics knowledge (-not listed?) - would you want to do a mainly analytical or a computational thesis? Keep talking to your...
Knowing 5y is in both equations makes it easy. Just take both sides of one equation away from both sides of the other and get a single equation with just "x" in - (have you come across solving simultaneous equations before?)
Think about what type of Engineering interests you. Would you look straight for employment, or consider doing a masters in engineering, for example, to improve your prospects. You could likely switch from Physics to large parts of engineering.
I'm in the fourth (final) year of a single honours mathematical physics Msci in the UK - about half maths, half physics. Obviously it'll depend on the syllabus at where you are, or where you apply to. I can only tell you about mine as an example (my uni is a large top10 ranked one) - I haven't...