OP: Now, one who is stingy and not even willing to master it, can such a person expect to be able to grow in Dhamma?
Could he even understand teachings a little in right way, and open to the next step, i.e. right moral virtue?
Only a Tathagata can tell whether someone be able to develop the path and get across samsara or not. There was a wealthy baron during Tathagata's time who was very stingy. But later he became a stream winner.
From the Pali Kanon Buddhist Dictionary of Proper Pali Names page on Maccharikosiya:
Maccharikosiya, A setthi, worth eighty crores, of Sakkhara near Rājagaha. His real name was Kosiya, but as he was too miserly to give away even a drop of oil, he came to be called Maccharikosiya. One day, when returning from the palace, he saw a half starved yokel eating a round cake filled with sour gruel. The sight made him hungry, but fearing to spend his money, he told no one, but lay on his bed in great distress, till his wife found him. Having discovered the reason for his misery, she said she would bake cakes sufficient for everyone in Sakkhara. "But that would be such extravagance," said Kosiya, and persuaded his wife to bake just one cake, using only broken grains of rice. Fearful lest someone should ask for a piece of his cake, he retired with her to the seventh storey of his house and there made her start the cooking after bolting all the doors.
The Buddha saw him with his divine eye and sent Moggallāna to him; Moggallāna stood poised in mid air just outside Kosiya's window and indicated his wish to have something to eat, but Kosiya blustered and threatened, and, after refusing to give him anything, bade his wife cook another little cake for him. But each cake she baked grew bigger than the previous one, and when she tried to take a single cake from the basket, they all stuck together. In despair, Kosiya presented cakes and basket to the Elder. Moggallāna then preached on the importance of generosity, and transported Kosiya, his wife and the cakes to Jetavana. There the cakes were offered to the Buddha and five hundred monks, and even after they had all eaten, there was no end to the cakes. The spot where the remaining ones were thrown away at the gates of Jetavana was known as Kapallapūvapabbhāra. The Buddha preached to Kosiya and his wife and they became sotāpannas. Kosiya then spent all his wealth in the service of the Buddha and his religion.
Note: This is how I understood. I may be wrong but not Dhamma.