The game has action + bonus action, typically doing something with the offhand (dagger or hand crowbow) will cost you a bonus action and in the example you gave, equipping the weapon from his storage also costs an action so yes that is totally in keeping with D&D rules
Your character can carry around a longsword & a greatsword but it takes time to swap between them during battle... With the right feat he could carry two longsword (dual them) which is also in the rules and my personal choice
