🚀 go-pugleaf

I am getting interested in compact 2-manifolds embedded in R^4.
Consider such a thing and call it S.  Let S_t be the intersection of S
with the surface {(x,y,z,t): (x,y,z) in R^3}.  If S is generic it seems to
me that for all but finitely many values of t, S_t will be a link in
R^3, and at the finitely many "bad" values of t S_t will be a link
with a single transverse selfintersection OR a link union a single
isolated point.  I guess we can use Morse theory to show this, taking t
as a Morse function and noting that there are 2 kinds of critical
points, saddle points and extrema, which give the 2 cases above.

There is a little about this in the section Knotted 2-spheres in an
article by Fox in Topology of 3-manifolds and Related Topics, ed. Fort.
The references there all antedate 1962; can anyone direct me to more
recent stuff, especially surveys?  Can anyone tell me what, if anything,
this has to do with Donaldson theory and link invariants?  

Can anyone direct me to similar stuff that treats the case of generic
immersed rather than embedded surfaces?  Generically an immersed surface
in R^4 should have some transverse double points and these should spice
things up a bit.  I would like to know how the picture I paint in the
first paragraph generalizes to this case; I *think* I know but haven't
gone through it carefully.

Of course, not only references but also general wisdom about this kind
of thing would be greatly appreciated.