Unless the DM chooses to deviate from RAW, most of these items do not have prices and therefore cannot be bought. Technically, without the DM making up values for these items, they also have no weight, deal no damage, and cannot be sold. In effect, they are non-physical character sheet decorations. Roleplaying props. Clutter. Eraser bait.
But maybe yes.
However, DMs make stuff up all the time for the sake of verisimilitude. Unless the DM is absolutely keen on PCs being permanently tethered to these Final Fantasy style immaterial "key items", they'll probably make up prices and weights, call the knife an improvised dagger, give the mouse the stat block of a rat, treat common clothes as a generic catch-all covering a wide variety of styles and appearances rather than an exact single outfit, etc.
But mostly no.
Just because "you can houserule it" doesn't mean it's univerally OK though. You can houserule anything under the sun, but the existence of DM fiat doesn't change the text in the corebooks outside of play, and one DM's eurika could easily be another DM's BS. So make sure your DM is involved in your character creation process. They are your only true connection to the world inside their head, and they're going to be the person adjudicating and modifying the rules and content for this character for as long as you play with them. Who knows what gear they might make available to players who choose to purchase equipment. There may be tons of homebrew items they've made up that they're just itching to see you use! Or they may hate that rule, and say all characters must take their starting gear. You'd never know unless they are involved. Keep your DM in the loop!