so here is the deal: when i start my car when its cold, it takes like 10-30 seconds to turn over... it cranks fine, but just takes awhile to turn over. when its warm it starts right away. i dont think its my starter, it sounds like its turning the flywheel, but just that the engine isnt firing... any guesses?

also- another ...sort of... related problem... so sometimes my car will start up and it will instantly die... i usually give it a little gas when i start it and even when i do that it just dies and it makes a sort of "hollow" sound its kinda hard to describe... then i wait 60 seconds... and it starts right up... but if i try to start it before that it just cranks and cranks but doesnt start... any ideas what this is about? are these problems connected?

thanks in advance