How the speaker knows: a report, an inference from clues, or both
Each one below is our full write-up of that form, in the order worth reading them. Nothing is summarised — you are looking at the same pages the grammar index links to, put next to each other.
seems like, is like
V-plain / い-adj / な-adj + な / N + の + ようだ（みたい attaches plainly）
Expresses an inference from clues, whether you observed them directly or learned of them indirectly. みたいだ is more conversational and attaches straight to a noun: 子供みたいだ.
Also used for resemblance and comparison: 雪のように白い — "white as snow".
seems, apparently; typical of
V-plain / い-adj / な-adj / N + らしい
Presents something as apparently true based on available clues or a report you have heard. It can overlap with hearsay そうだ when passing on something you heard; the contrast is not simply firsthand versus secondhand.
After a noun it can instead mean "typical of ~": 男らしい, 春らしい日 — "a real spring day".
I hear that ~
V-plain / い-adj / な-adj + だ / N + だ + そうだ
Passes on information heard or read from another source, rather than an impression from immediate signs. It attaches to the *plain* form, unlike the looks-like そうだ. The speaker may still have an opinion about the news.
Compare: 雨が降るそうです (I hear it'll rain) versus 雨が降りそうです (it looks like rain).