Home DIY

we could then close up gaps when re-laying the boards,

Only do this if you are replacing original boards with a modern flooring system. Timber boards will expand and contract seasonally this is why they were originally installed with a gap. The movement is why traditional floorboard are laid with gaps between them, gold standard is a 2mm gap but this won't stay like that for long. People often fill between boards when sanding and finishing traditional boards but this won't last too long.

Is it worth removing the original/old nails and later putting back with new ones?

Yes. It's essential, but you could reuse the original cut nails if they aren't too rusty.

so not have to worry about original nails going into original holes in the joists.

You shouldn't do this for 2 reasons:

1. You'll drive yourself mad trying to reassemble a very boring, hard jigsaw puzzle
   
2. The nails won't hold that well - for nails to work they need to go into fresh holes that they create.
   
   

If worth getting new nails - any particular ones? Or use a nail gun of some kind?

Ringshank nails will hold the best 50mm should hold well - personally I'd go stainless if you can find them if not hot dipped galvanised

Would be quicker if you're using a nailer (first fix) but the tip will mark the wood, if you do use one remember to ventilate the space you're working in also, hearing protection and wrap around safety squints are a must. I'd strongly advise you spend the time accurately setting the depth of the nail heads before mailing boards down.