I found that R Sinai was Rav vidawa 1829 - 1835, he wroth a hesped on rabbi Meir Tzilch rabbi of Lask who was niftar in 1826, he was traveling with the Chidushei Harim and Rabbi Yeshaye Mushkat of Prag to Koznits to Rabbi Moshe Elukim the son of the Magid of Koznits (niftar 1828).
As of a conclusion R' Sinai was born about 1800 - 1805, I don't think that he was Rav in vidawa when he was under the age of 20, he was most probably in the age of the Chidushe Harim.
His father R' Elazar was niftar before 1835, in the yizkor book of Lask page 148-139 https://archive.org/details/nybc313850/page/n150 is mentiond that R' elazar was magid meisharim in Lask, when he was niftar R' avraham Liichtshtein was magid in Lask, R' avraham was niftar before 1835, that we see on the haskamos that was writen in 1835 to the sefer kanfei nesharim from R' avraham Liichtshtein.
I was just doing some research on R Sinai and I came across this page so i thought to write my findings here it will be useful for you.
