I’ll quickly try to explain all the questions raised.
A chain combo is very similar to a regular cancel combo i.e. cr.mk xx fireball, but you are basically cancelling one normal with another (also a bit like target combos).
Now in general, a regular cancel combo (like cr.mk xx fireball), all the recovery frames of the cr.mk are removed/cancelled and replaced with the start-up frames of the special move.
I don’t have the exact frame data but lets imagine that a move has 4 frames start up, 1 active frame and 4 frames recovery. Now a cancel combo would cut the last 4 frames of this first move and replace them with the start-up of the special move.
Chain combos are almost exactly the same but they do not remove all the recovery frames, they tend to cut in a few frames from the end.
This is why the timing for cr.lk xx tatsu is slightly different to the cr.lk, cr.lp chain.
This also explains why Ken’s cr.lk, cr.lp chain has different timing to that of Ryu’s as the frame upon which the cr.lk can be “cancelled” is different.
All Ken’s light attacks can be chained into each other, including cr.lk, st.lp and cr.lk, st.lk.
st.lk has 6 frames start up but can be comboed from a successful cr.lk (which is only +3 on hit). Why? Because a proportion of the recovery frames from cr.lk get removed when you successfully chain the st.lk.
Just as an interesting point, cr.lk, st.lk is not a true block string (you can mash out a DP between them)
Chain combos are generally quite leniant with their timing (slightly stricter than a cancel but way looser than a link), but they are different for every character. From memory, the Ryu chain timing is significantly different to Ken’s.
Hope this all helps.
Peace,
G.