You don't have nearly enough to sustain ricochet and boomerang blade. EVERY Sivir worth a damn builds an early chalice or manamune for this reason.
Warmogs is a terrible item on any champ that Sivir doesn't need. Hexdrinker + spellshield + chalice/mercs MR will keep you alive against magic damage. If you need more durability against physical damage, randuins is your best option. More relevant on the issue of durability is that you don't build any defensive items until after the BT and LW. Sivir only farms fast if she can stay in the lane. The specific defensive items that you pick aren't super-important, as you should have the gold for anything you want, but getting them at the right time is much trickier and much more crucial to the early and mid game. I, personally, am quite partial to building a hexdrinker in between my chalice/mercs and my BT.
AS quints are awful, and ARpen gives more damage than AS does anyway, though I prefer hp quints as I find Sivir benefits more from the extra staying power early. CDR blues and mana regen yellows are good, though if you grab a mana regen item early (which you absolutely should) than you can afford armor or dodge yellows.
I really don't find mana a problem. If I run low on mana i can normally use my spell shield to regain a bit of mana or I just dont use my boomerang much for the first few levels of play. It just seems a waste to build a mana item when it isn't really needed.
- Run desolation (arpen), not alacrity (attack speed) runes. - Running mp5 gylphs and seals is more optimal imo. - Skill order should not be rigid (e over w in some cases) - If you are getting a HP item that late, grab a mallet. I love mallet on Sivir in any case.