Thank you!! So for instance, i have Pisces Sun in 4th house; and Leo in 9th house.
Is the Neptune the ruler of my 4th house (given Neptune is the ruler of Pisces)?
I would follow the traditional recognition of Jupiter's rulership of Pisces, so Jup would rule your 4th.
Or is rather the Moon the ruler of it (given that the Moon is the ruler of Cancer, and that there is an issue of Cancer house being the 4th)?
Moon rules the house in your natal chart whose cusp in the sign of Cancer. In terms of rulership, Moon has no particular association with the 4th.
Also, given that my chart has Leo in the 9th and that the Sun is Leo's ruler,
is it right to say that the Sun is the ruler of my 9th house?
Very good! Yes, that is correct.
Saturn is in Leo (9th house), so what is the influence of the Sun over Saturn? Or tu put it differently:
is it right -)) to speak of such an existing relation?
Yes, it is appropriate to consider the influence of Sun over Saturn as follows. Sun has rulership over everything in the sign of Leo. So Sun rules your 9th as you note since its cusp is in Leo. Sun also rules Saturn which is in the sign of Leo as well..
Thanks
Ps: i was typing while Ilenek message was sent; thank you both!!