What is the lifespan of the car seat?
It very much depends on two factors - which car seat you mean / you get to complement the stroller system (it can be a Maxi-Cosi Cabrofix, which is one of the largest one on the market, or it could be a cheaper one which often are much smaller), AND it also depends on the child. It is very different from baby to baby, and one, born larger or one that grows quicker will grow out of the car seat considerably sooner.
If we're talking about the Mothercare car seat that is included in some sets, it is a kind of no-name car seat so don't expect much. It is simple, and it will, in general (with an average baby), last you about 6 to 10 months of age in reality. Again, depending on the child, but also the season (it is very different in thicker, e.g. winter clothing), it won't really last you until the 13 kg weight capacity they state (they mostly don't, to be honest).