Seatpost

if you think about the actual amount of deflection - i.e. movement and ability to absorb shock - in a regular seatpost then you're really talking a few millimetres if that. I'd be surprised if you could really measure it. without some specialised equipment. You'll get more real benefit from some fatter tyres (28s) on a lumpy road.

However to answer your question then Deda stems and seatposts are hard to beat for the price, better quality than FSA and Easton for less cash IMPE. Something like the Deda RSX02 can be had for around £22 or so

Neither is cheap, but I'd probably go with a Specialized Cobl Gobl-R or a Canyon VCLS Post 2.0. Both are designed to take the sting out of cobbles but, if your sportive is Paris Roubaix, you'll need more than a seatpost (a chiropractor!).

Depends on your frame.

I tend to mix titanium with carbon to cover the bases (there is absolutely no scientific research to back me up) in terms of "frequency" of road buzz. I have a Ti frame with a carbon seatpost, although I swap it out for an alloy one when the big saddlebag goes on. If I'm honest, it makes little difference other than in weight.

If you have a carbon frame anything other than a carbon post is likely to attract funny looks.

If you're on steel then, again, either will do.

If your riding an alloy frame on cobbles, it doesn't matter, you're friar tucked. Your arse will start to bleed after a couple of miles regardless of what you have as a seatpost.

For alloy posts I recommend Nitto or Thomson and for carbon, FSA or any of the major brands so long as you avoid the cheapest end of the market ie spend at least £60. There are other options in Ti, but it's a £100 starting point for them.