Just wondering whats the normal time you pick up Heart of Gold? Like under 10 min?

I normally get a Philosopher's Stone as my second item, but start with another item first (Meki Pendant, Mana Manipulator, or Doran's Ring, most likely). I usually don't get a Heart of Gold, because I don't plan on upgrading it. Unless I want a Randuin's Omen, then I will. Sometimes I'll get a Kage's Lucky Pick if, for some reason, noone on my team has ignite and they have something annoying like Soraka.

It really depends on a lot of things. How much warding/counterwarding I feel is necessary for my lane (I ward a LOT more against Blitzcrank/Alistar/Taric/Leona for fairly obvious reasons). Whether or not I take any CS that my partner misses. Whether or not we get any early kill money.

In some games I've not gotten the HoG until the 18 minute mark. In some games we do amazing early game and I have it by the 7 minute mark. Along with the more important Philo of course.

Pendent -> Phil -> boots 1 -> HoG -> boots 2. Sometimes I'll get boots before Phil if I need to back or die before I have the cash for it. This is my typical starting build whether I play Taric, Ali, Janna, Soraka, etc. I sometimes get HoG with support Blitz but only if someone else gets Aegis (e.g. Shen top or jungle Amumu).

HoG is a good item to rush even if you never upgrade it as life is most useful early. These items get your GP 10 going, make you a bit tanky (assuming some defensive masteries and runes), solves your mana problems and lets you absorb some harass. All quite cheaply too.

That being said, sometimes I'll throw cloth armor or something before I get HoG depending on how the lane goes.

HoG is a great item for pretty much every support. It’s not as important as a Philo stone but the extra gold and hp go a long way toward keeping you alive and getting some better items. I also go Philo – boots 1 – HoG – Boots 2 then I will build some completely different item like Aegis of the Legion. This lets you keep the gold bonus longer before you finally build them into mid to late game items.

I try and aim for philo boots and hog somewhere around 10 minutes give or take.

Every game. If you play a support tank (taric, Alistar, ect) you want Randuin's anyways, and for non-tank supports it's still survivability. If it really bothers you that much you can sell it later and it'll probably cover it's cost. Depends on how fed you're getting.

But even supports like Karma and Soraka can find a use for it.