I promoted to Silver 5. I lost 1 game at 0 LP, then won a game, then lose two games that put me back at 0 LP.
If I lose again do I drop to Bronze 1 now? or do I still have more chances?
Edit: Does the fact that I won a game ruin my grace period before being demoted?
Your MMR needs to drop to Bronze before you demote. My friend was silver 5, but it took him going 4-24 before being demoted to Bronze 1.
Your MMR needs to reach the bottom of the pit, by that I mean literially bronze 5 or 4.
5 games at 0 lp before you drop. Unless you are at any tier 5, in that case you have about 10-20 losses before demoting.
Is there any warning before you demote? or does it just happen? like if you're one loss away is it like, hey you lose one more you demote?
I'm not sure about now, but I think there is a 10 game shield when you go up a tier.
There is a shield, and your MMR would have to tanke on whole tier lower (bronze 5), and there is a warning prior to. This is from the Ranked FAQ, congrats on your promotion. Welcome, to silver, it's much much worse. 
HOW DOES SHIELDING WORK? Temporary shields will stop players from dropping into a lower tier immediately after promotion. You will be shielded from demotion for the next 3 games after you advance a division. If you advance a tier, you will be shielded for 10 games (3 games for Master Tier). Furthermore, if you are in danger of being demoted to a lower tier, you will receive a warning in your Summoner Profile. They will look like this:
I would add that if you stay in silver for quite a while but have an overall poor win ratio, it will take fewer and fewer consecutive losses at 0 LP to drop to bronze. I finished placements (this is my first season ever to play) I was in silver 2. I almost instantly dropped to silver 5 and hovered there for about 2 months.
My overall win ratio at that point was only around 40%. I kept bouncing between 0 and 30 LP. When I dropped, it only took 3 consecutive losses at 0 LP to drop me to bronze. And from there I tanked to bronze 3 0 LP in a single day. Seriously, check out the losing streak I had over the July 4th weekend. It gave me PTSD.
Climbing out of bronze was really, really tedious. Once I got back to silver it's been a pretty easy, steady climb, and I'm almost back to S2.
