
Ben M. answered 04/12/19
Japanese/ESL tutoring from an accomplished translator/interpreter
Good question!
First things first, デイビット is one of several ways to write the name David. I know a few Davids/Daves with Japan experience, and I think almost all of them write their names differently--the joy of having options!
When you're talking about 〜そう, 〜よう, and 〜らしい, you're correct that there's both overlap and difference in nuance. This is an easy topic to dive deep into, but the fundamentals are simple.
1. 〜そうです
As you know, there's a difference between 〜そうです used to report speech and 〜そうです used to convey personal observations based on direct sensory input.
デイビットは料理が上手そうです <--It looks like David is good at cooking
デイビットは料理が上手だそうです <--I hear David is good at cooking/Apparently, David is good at cooking.
With that out of the way, the main point of 〜そうです when you're expressing sensory input is exactly that: You need to be looking at or hearing whatever you're basing your impression on. If you're not looking at or listening to something, you're less likely to use 〜そうです.
However, you can easily say something like 大変そうです! in response to someone telling you something. Like if I say, "My pirate ship exploded and I was attacked by flying bird sharks while I was in the water," you can respond with 大変そうです! ala "That sounds terrible!"
2. 〜ようです
〜ようです functions (almost?) exactly like "seems" in English. So just like in English, you can say something "seems" to be the case if you're looking directly at it, but you can also say something "seems" to be a certain way if you're just speculating, even if you're not looking directly at whatever you're talking about.
デイビットは料理が上手なようです <--David seems to be good at cooking/It seems that David is good at cooking
If you say this sentence, you have reason to believe that David might be good at cooking. It could be that you're watching him cook, or maybe you've seen a dish that he's prepared, or maybe you heard that David won a cooking contest. In all of these cases, just like in English, you could say "It seems that David is good at cooking."
3. 〜らしいです
〜らしいです is probably the most "uniquely Japanese" of these three expressions, since the nuance conveyed by 〜らしいです usually doesn't even get translated into English because it's considered unnecessary.
In a nutshell, 〜らしいです means you've *heard* that something is a certain way, or you have *reason* to believe something is a certain way, but you have no firsthand sources. A firsthand source would be, for example, that someone directly told you, or that you saw something with your own eyes. But if we're just saying that "rumor has it that a cat barfed on the rug, but nobody here owns a cat and I'm not even sure why anyone's thinking that," you could just say 猫が絨毯に吐き出したらしい.
The big difference here is, if you say 猫が絨毯に吐き出したようです, you have a concretely specific reason to suspect that a cat barfed on the rug. But if you're reporting secondhand speech, or information from a similarly vague inference/source, it's most appropriate to use 〜らしいです.
I hope this helps!