robot

From the Czech word robota 'servitude' < rab slave'. Our word slave is from the (Latin) ethnonym Sclavus Slav' (cf. Russian слава, slava, 'fame', слово, slovo, 'word') < PIE *kleu- 'to hear'. And serf is from latin servus 'slave, servant'

silent t

I have never heard this, but it makes no sense at all. The word robot is a borrowing of the Czech word robota in which the t is pronounced. Besides androids and automata, there was the medieval Jewish story of the Golem (Yiddish goylem) created by Rabbi Loew of Prague. In French, robot is pronounced without voicing the t, but as the play R.U.R. was translated from the Czech (by Paul Sever who also translated The Good Soldier Švejk) and not the French, I cannot see how this has any bearing on the English pronunciation.

Ceci n'est pas un seing.