I love everything about him, his design, his kit. I played a game vs an Annie and I fed like 6 kills in lane (in my defense our ADC was afk and Bard had to solo lane bot while I was being camped by Nidalee) (not in my defense I gave FB because I was overconfident/tunneling and took two turret shots. but that's an easy mistake to fix). How do I improve?
Wards are always a solution to being camped by the enemy jungler or anyone else. Also, simple map awareness!
If you're getting harassed hard in lane just play passive and try to farm under tower, if they are still pushing hard, signal your jungler for an easy kill or to blow there flash, also giving you time to farm and back for items!
Good luck, hope I could help you! 
The worst thing about Vel'Koz is that he is very immobile. You just need to land your skillshots, especially your knock up. Don't waste your knock up at all, save it for moments you know you can land it. If enemies are able to dodge it (especially Annie) you will not have a fun time since they'll be in your face and you don't have spells to run.
if your vsing annie get abyssal asap for mr defense and ap damage under her shield. play defensive offensive amping with rabadon at 3-4 item
I always pink the banana bush to the left or right side of lane that peeks into river, ppl never look there.
When i mained vel, i had a rule that i was never allowed to go past the center of the lane, no matter what. Movespeed quints ive heard are nice b/c its more useful than ap b/c his scaling. I max W for waveclear and rarely try for kills unless the jungle ganks or the enemy misplayed very hard.
Someone said abyssal, but i cringed. The AOE mr reduc. is smaller than his q range and ult range so i dont like it. I have a rule that even if i dont need it now, i rush zhonyas or QSS if i think i will need it soon, so it can save my life earlier and i dont die b/c i dont have it. And better than abyssal, athenes. Its mr CD and mana regen, or just leave it at chalice if you want zhonyas, but spamming w+w keeps the creeps off your tower if the enemy keeps on pushing.
Hope I helped :)
