Not a specialist in physics but I still think I can help with some of this.
About plank length/time: this isn’t the “smallest length/time that exists”, it’s just a limit under which we know our commonly used model for distance and time stops making sense.
To help you understand this, think about something such as temperature: you probably have an intuition about it (unless of course you are like me and your perception of temperature is completely screwed up), you can feel that some things are cold and some other are hot, and you are probably able to imagine what would it be like to have something “hotter than this” or “colder than that”. From that you can imagine temperature as a property of matter.
Now take a blob of gaz (one that is, let’s say, at 20°C). Cut it in half: both of the two halves will be at 20°C. Cut it again: still. Imagine an ideal cutting tool, one that lets you cut extremely thinly without adding heat. When you reach chunks of sizes around a few molecules, this notion of temperature stops making sense: temperature simply only makes sense for stuff that is composed of enough small elements that we can’t consider each of them individually. To say it differently, if we were able to know precisely the state of all the molecules in a room, then the notion of “temperature of the room” would stop making sense.
Distance and time are somehow like that: they work fine for most of the stuff we encounter in our everyday life, but we also know they are not a perfect description of the details of what happens.
Not a specialist in physics but I still think I can help with some of this.
About plank length/time: this isn’t the “smallest length/time that exists”, it’s just a limit under which we know our commonly used model for distance and time stops making sense. To help you understand this, think about something such as temperature: you probably have an intuition about it (unless of course you are like me and your perception of temperature is completely screwed up), you can feel that some things are cold and some other are hot, and you are probably able to imagine what would it be like to have something “hotter than this” or “colder than that”. From that you can imagine temperature as a property of matter. Now take a blob of gaz (one that is, let’s say, at 20°C). Cut it in half: both of the two halves will be at 20°C. Cut it again: still. Imagine an ideal cutting tool, one that lets you cut extremely thinly without adding heat. When you reach chunks of sizes around a few molecules, this notion of temperature stops making sense: temperature simply only makes sense for stuff that is composed of enough small elements that we can’t consider each of them individually. To say it differently, if we were able to know precisely the state of all the molecules in a room, then the notion of “temperature of the room” would stop making sense. Distance and time are somehow like that: they work fine for most of the stuff we encounter in our everyday life, but we also know they are not a perfect description of the details of what happens.