The Vayne was kind of a jerk to be making fun of you. Helping/suggesting different ways would have been better. I'll try to hit on all of your topics, but as I'm only gold I, anyone who has a better understanding please feel free to correct me:
The old jungle was fairly easy to clear for the popular champions, meaning they would hit level 3 rather easily and have enough HP left for a quick gank. This led to supports commonly bringing a vision ward so that they didn't only have to rely on coordinating trinkets with their ADC. While you may still see this today in competitive/duo queues where there is a planned invade, having 4 pots to be able to stay in lane has become more standard. This is because the junglers only start off with 2 health pots now due to gold changes, and most cannot sustain enough to gank early. Therefore being able to stay in lane and get experience becomes the primary focus, and if you can out sustain your lane opponents in trades you should end up winning lane.
Summoners
On the same idea of trying to out sustain your lane opponents to have a bigger CS/EXP advantage, you don't want to be taking a summoner spell which has little to no combat use. If your lane opponents are running some combination of Heal, Exhaust, and Ignite, this puts you at a serious disadvantage should you ever try to all-in for the kill, or be all-inned yourself. With the meta currently shifting away from hypercarry champions (Trist, Vayne) to more caster ADC's like Corki, Graves, and Ezreal, Ignite is generally the summoner of choice as these champions generally deal too much upfront burst damage that exhaust doesn't mitigate it. That being said, if you are confident you can win lane, Exhaust is still a great choice as it can be popped on anyone who is wrecking your team in the lategame teamfights.
Laning as a Support
Personally, I think it depends on what your ADC is comfortable with, but there are things you should be paying attention to. When you say you hit the minions once for your ADC, I hope you mean when they are under turret you hit them once to allow your adc to get the cs. If it's out in the middle of the lane, your ADC may prefer you not to hit them at all because this can mess up their plans for last-hitting as well as put them at a disadvantage if the lane pushes at an inopportune time.
Harassing your lane opponents is always a good idea, however running out of mana is bad. Rather than take Clairity, try using autoattack harass. Especially early levels when armor values are low, good auto attack harass can do far more damage than spell damage. Save your spells for when you are engaged upon to keep the trades in your favor. If you are playing as Lulu, this means auto-attacking and using your glitterlance to slow your enemies and put them out of range as they chase you, or even polymorphing them in a 1v1 since they'll be doing no damage in cupcake form.
Standing in Bushes depends on the support. An unseen Thresh/Blitzcrank generally poses far more risk laning against than an easily visible one, however even as lulu you hold decent respect hidden in a bush. As long as the bush isn't warded, when you are guaranteed the first damages in trades, such as starting them from fog of war, you generally stand a much better chance in winning the trades. But to have lane presence you will sometimes need to come out to scare your enemies. I tend to think of it like this: If I run at my enemies and they try to retreat, I'm better off out of the bush and just hiding for a few seconds at a time. If I run at my enemies and they immediately want to trade damage, I'm better off spending more time in the bush, coming out to harass as needed.
Support builds
The build you listed is fine, if you were a solo-lane Lulu where you were actually being funneled the gold. Due to supports not getting CS, the power spike associated with these items is too far delayed for Lulu to make much of an impact. One of the big benefits to support is being able to control vision around objectives. Sightstone is good, but after listening to Krepo's reasoning, I generally prefer to rush Mobility boots first and keep buying wards until I finish my sightstone afterwards. The explanation won't fit here due to character limits, but I highly recommend watching this video he has talking about supports/vision:
https://www.youtube.com/watch?v=K4EfueGH7IY&feature=youtu.be
As for other items, your goal as support is to either engage on the enemy or peel for your carries (depending on who you are playing). As Lulu, with her kit of shielding and slows, you generally want to act as peel for your carries. Recommended core items are
as this will provided extra resistances, shielding, and a cleanse from CC for a single carry. Aura items are solid, but builds should be tailored to the situation you are in. If you're against an all-AD team, you might forego
in place of
or 
Hope this helps!