the Basic Usage section doesn't have anything but 見える written - shouldn't it be something like [Noun] (or [Prase]) が見える?

Why does this answer use に and not が?　

私 に　 は　 彼かれ は　 とても　 やさ しい 人 に　 見 えます 。　

Shouldn't the 'looks like' form be separate? I came to look at the notes here because I was also confused by that exact sentence. It seems that knowing it should be に there doesn't have a lot to do with understanding that 見える means 'can be seen'.

Can these be added as well for number 2?
Verb-てform + 見える
Verb-casual, non-past + ように見える

陽が、またたくまに背にしてきた木々の中に沈んで行くように見えた。
Almost at once the sun seemed to sink into the trees behind me.
hi ga, matatakuma se ni shite kita kigi no naka ni shizunde iku you ni mieta.

私には、彼は少し腹を立てているように見えた。
I could see he was a little upset.
watashi ni wa, kare wa sukoshi hara o tatete iru you ni mieta

Found it in Nihongo Bunkei Jiten (pages 555-556). It appears to be a short-hand for the above examples:
疲れて見える = 疲れたように見える = looks tired

There are also some examples in the site's sentence library, such as:
彼は年の割には老けて見える。 - He looks old for his age.
今日はいつもと違って見えるね。 - You look different today.