Insurance length only takes affect after full game v1.0 launches which is more than a year away right now.

If you spawn in and your ship is destroyed just file an insurance claim for free at the ship console where you normally request. There might be a minute or so delay for it to be replaced. But with a starter ship it should be instant. Some larger ships have a 15-30 min wait or a 5 minute expedited time if you pay in game money.

There are still a lot of bugs that can lose you your ship but until it goes full 1.0 release your ship insurance wont count down. No worries there. On the flip side though every major patch will reset your in game progress. So if you save up in game for a new ship youll lose everything you earned when 3.4 releases. Major patches release every quarter so youll reset 4 times a year minimum.

One of the reasons people buy bigger ships with real money is so they dont get reset to just their starter ship every patch. Kind of makes the game pay to win in its current state.