She clearly says (book 6) she is afraid of the gossip if she comes home with a strange man.
he said that he didnt want to be seen with her for fear that her father would get mad
No, Odysseus was already married to Penelope. Further, Nausicaa did not want to marry Odysseus.
I'm pretty sure Odysseus but he declines
Alcinous feels that he and the stranger "think as one."
Nausicaa will not let Odysseus ride in her cart because she is trying to avoid rumors about them. She is following the rules of propriety and doesn't want people speculating over her connection to this stranger, especially since she is looking for a husband.
She doesn't want people to gossip about him being her future husband.
Cdyfyf
In Book 6 of the Odyssey, Nausicaa asks her parents for permission to take the clothes to the river to wash them, after her dream about Odysseus. She seeks their consent as her actions may attract unwanted attention and criticism from society.
because Odysseus blinded him
For the cheesiest reason possible: he loves only his wife, he misses her, and wants to go home. I would think that would be obvious as that's the reasoning he gives Circe.
he want to save him
The men gathered there are suitors and they want to marry Penelope, Odysseus' wife.