Filling cracks in stairs, and affordable runner fitting

Galileo_Figaro

I need to take the carpet off our stairs ASAP as the final part of remediating a mould issue (causes now resolved). In the long run we want to get the stairs sanded back to wood, but can't afford that at the moment, so I'm looking for an affordable fix (also a pretty safe one - we have a four year old). Two things I'd appreciate thoughts on:

1. There are some gaps in between stairs I need to fill to make sure the air is fully separated from the coal store below. I know if we waited until sanding then we could fill them with sawdust and glue, but that's a few years away. Has anyone tried to colour match caulk and do it that way? Or any other ideas?

2. Has anyone had success with fitting a stair runner without nails, staples, or anything that makes holes in the wood that would show up when we get to sand it down and expose the wood?

Thanks