Were there religious jews of the Torah/the Covenant outside Jewish sects on the time of Jesus? How did they exercised their religion?
All of the Jewish "sects" (Sadducees, Pharisees, Essenes, Samaritans, Zealots) would have understood themselves as 'Jews of the Covenant' and Torah observers.
The ordinary "lay" Palestinian Jew who was not schooled in any of these sects would have:
- listened occasionally to some famous rabbi that came to town, perhaps hoping to see miracles or have some of their problems solved;
- gone out to the desert to see an extraordinary prophet like John the Baptist and perhaps receive his baptism to break up with sin and start a new life;
- made his pilgrimage to Jerusalem for the Great Feasts to 'appear before the Lord' at the Temple and bring his sacrifices; if not 3 times every year, as the Torah required of all men of Israel, then at least once or maybe several times in his lifetime;
- attended the local synagogue on Sabbath, where the Torah was read out in Hebrew (which he wouldn't have understood much) and then translated/paraphrased by a meturgeman
(interpreter) in his native Aramaic;
- roughly adhered to the prescriptions of Mosaic Law and Jewish customs (circumcision, marriage, death & mourning);
- expected the Messiah to free them from Roman occupation and restore the Kingdom of David to its former glory.
The Pharisees would call them 'am ha'aretz
(people of the land/country men/peasants), ignorant in the ways of the Torah, and Jesus took pity on their multitudes and viewed them as "sheep without a shepherd".