Yes: appear to be, have the appearance/air of being, give the impression of being, look, look as though one is, look like, show signs of, look to be; come across as, strike someone as, sound.
"Seems" is a verb.
Seems is the verb. To be tired is a verbal phrase, a verb form functioning as another part of speech in this sentence.
Yes the word seems is a linking verb
The verb in this sentence is "seems."