They are of course, intimately related. Degree of
dissociation is to be calculated or derived from Ka, the
acid dissociation constant, which is fixed for any given acid,
at a particular temperature.
Your 1st point is correct, but it is really an issue of
technicality rather than Chemistry concept. Ka is direct,
dissociation degree is indirect and derived as a
result. Hence, Ka values are more useful.
Your 2nd point is partially correct; there will necessarily be
different degrees of dissociation for dibasic (diprotic) and
polybasic (polyprotic) acids, depending on whether you're referring
to the 1st acidic proton, the 2nd, and so on. Just as there is Ka1,
Ka2, etc.
As far as the H2 syllabus is concerned, you mainly need to
work with Ka. Possibly, the question (in the 'A' level exam) might
ask you to obtain the degree of dissociation, given the Ka
value.
Simply use 'alpha' or 'a' for degree of dissociation in the ICE
table; where c = molarity/concentration in mol/dm3 of the acid.
_____________HA ---> H+ + A-
Initial
c
0 0
Change -ca +ca +ca
Equilibrium
c(1-a)
ca ca
Hence, substituting Ka value into the Ka expression (that is
based on the equilibrium molarities of the ICE table above), you
can work out the value of the degree of dissociation.
There are quite a number of acid-base equilibria 'A' level
questions that can be done by two alternative working
pathways. One alternative working involves degree of
dissociation, the other (alternative working) without using
degree of dissociation, but in moles directly (ie. not percentage
dissociation). Both alternative methods will give you the
correct answer, it's up to you which you prefer to use in the 'A'
levels.