Compost and fertilizer use-by date?

Don't know whether they do deteriorate, but I'd use them!

I think shops have to be.

As for compost, if it's unopened then it won't be in too bad condition; you might want to consider adding fertiliser slightly sooner (usually it has enough for 6 weeks of standard plant growth), but it's unlikely to have become contaminated such that it's unsuitable.

Put it this way, plants survive without any fertiliser at all.  You've got nothing to lose by applying some free fertiliser ...