What to do with extra gold? Should you sell items and buy more expensive ones?

upgrade these please

But should you sell your items for other ones, like more expensive ones?

I normally don't sell my boots, but on katarina I guess you might consider because you'll be jumping to places anyway and you either die or you kill them all in teamfights. Not sure what to replace it with, though. Probably if their team is rather beefy, or if they have multiple squishies with low MRes and/or if their magical dmg is the main source that hurts you.

have 10k gold? simple solution! sell everything and buy more .

Depends really.

End game it's pretty logical to swap out defensive items to fit the situation, like who the current threat to you is, using GA ensure you're around for the next team fight, or picking up a Banshee's to prevent immediate lock down during a push to win.

As Katarina, since you have Luden's giving you a fairly massive MS boost, you can probably swap out your boots. Myself I'd probably get an Abyssal Scepter. As a short range APC the MR debuff aura will always be useful, more so than Sorc Boots passive, along with a nice chunk of AP and MR. (But I don't play Kat, I'm just giving an example (and I love Abyssal Scepter)!)

Also yeah, always be refreshing those elixirs.

It depends on the context of the situation. Sometimes, boots might not be necessary late game, especially if you're trying to get that one last push against a stubborn defense near the nexus.