how did jesus know the lady at the well was a samaritan?

This is conjecture based on fact, but sumptuary laws have existed from ancient times, and were certainly enforced in the Roman Empire. These laws regulated the fabrics and designs different groups of people were allowed to wear. Maybe Samaritans were either legally or culturally bound to wear different clothes from other groups.

Without saying that He is God?

Without saying that just with a quick pray He could get any answer He wanted from the Father and/or the Holy Spirit?

Jesus just probably saw her and recognized the style of clothing used by samaritan women.

he was in the territory where the samaritans lived

only Samaritans lived there no pure person of israel lived among the samaritans they were hated by the jews

the woman also tells jesus she is samaritan

KJV: John 4:9. Then saith the woman of Samaria unto him, How is it that thou, being a Jew, askest drink of me, which am a woman of Samaria? for the Jews have no dealings with the Samaritans.

It is not too hard to figure out if you read the preceding verses. "He must needs go through Samaria". The really odd thing is that the Jews hated the Samaritans because they were only half Jewish. They would go miles out of their way to avoid setting foot on Samaritan soil. But Jesus went through Samaria. He did not go around like everyone else. He knew that this woman would be at the well and He went through Samaria to minister to her.

He knew because all the fullness of God dwelled in Him

and He is omniscient . . .

Same as Jesus "saw" Nathanael under the fig tree before

Philip called him . . . and he was miles away. ( John 1:48 )

Well, Jesus is God. God knows everything and everyone. Lol. He even knew she had been with 5 different men, and the man she was then with wasn't her husband. He knew everything about her. Like I said, He is God. He knows everything about you and I and everyone else, too! God bless

Samaritan women were not shy about showing off their heafty cleavage.

If you meet someone in New York they are a New Yorker.

because jews would not be caught dead at that particular well

only facts ok here is one the fact is jesus was never real!