mama, if you are getting weeds, etc. sprouting out of your compost it not only needs to be turned it also needs something to heat the pile…MANURE, animal manure!  Do you have a source for that?  Horse, cow, chicken or anything close should be good.  When the pile heats from the manure it kills all the seeds.  You also need to keep it not to dry and not to wet and be sure to add as much browns (dried plant material) as you do greens (green plant material or kitchen scraps).  You can use some shredded paper to help with the browns if you don't have much.

I agree w/buckeye….use newspaper or cardboard to lay down to smother the weeds coming up.  I use several sheets of paper if I'm using that.  Just wet it as you go & lay something on it to hold it in place…rocks, dirt, boards, anything available.  I like cardboard better..it is easier to walk on without tearing and will stand up to rain & lots of other things and blocks all that heat better.

If you're careful to not turn in the shavings into the soil you can use shavings (many do).  Decomposing wood takes a lot of nitrogen that the plants want.  If you just lay it across the top, the soil underneath still has the needed nitrogen.

As for Cedar, well, I find cedar mulch available for sale, so my guess would be it's fine.  If you think about it, any tree that falls then decomposes and makes up dirt.  You may need to check pH eventually, but not at the beginning. 

The biggest consideration is for anything treated to the wood, which you say is not so.

Yes you can use wood shavings, but do not use much if it is fresh… you need to let it age and dry out before it is an effective mulch.

I used grass clippings for the first time last summer and LOVED the results. Just be sure and weed well before you lay down the clippings.  Also, I saved my leaves from the fall before, lightly mulched them and spread them in my flower garden. They did a fantastic job of keeping the weeds out and looked great. I will never again waste money on store-bought mulch.