Something in song, bathtime and in flight

I once was a house beneath the blue, now I'm a gift on the beach for you. My first three are large and salty, I share my next five with an oil company.

Every dawn begins with me, At dusk I’ll be the first you see. And daybreak couldn’t come without What midday centers all about. Daises grow from me, I’m told. And when I come, I end all cold. But in the sun I won’t be found, Yet still, each day I’ll be around. What am I?

He stands beside the road in a purple cap and tattered green cloak. Those who touch him, curse him.

In science I measure, in earth I reside, on skin I appear, though small I may hide. From numbers to tunnels to marks you can see, one word defines all versions of me.