Oil consumption

Okay, so 350 miles is about 0.36 quart and the 1000 km is about 621 miles.
So about of a 0.57 quart per 1,000 miles.
Normal is about one quart per 2,000 miles, so you are just about at normal.
The oil should turn black after a while, that means it is doing its job.
If you do believe the oil consumption is high though, perhaps you could try running some Gunk motor flush through the crankcase and free up any sticking piston oil control rings. Stuck oil control rings because of gunk/carbon buildup would cause excessive blow-by and too much oil consumption as oil passes by sticking oil control rings.
What you do is put in a pint of this motor flush, before an oil change, when the engine is cold. Start the engine, allow it to idle for five to ten minutes, drain out all the oil and cleaner, replace the filter and fill with new oil.
This is the stuff:

I would stick with the weight that your manufacturer recommends.
I unfortunately I do not have access to any repair manuals that cover the i30 because it is not marketed in the USA.
Try the flush first though. If it still consumes too much oil then I do not see why stepping up to 10w40 would hurt, especially in the summer time.

Could change to 10w30 or 40. The first number represents when the engine is cold the oil gets thinner for easier starts. Check around the engine to see if you see any wet spots. Could be anything from a slight valve cover drip or rear main seal drip.