rough idle on cold, vaccum leak? Please advise, thanks

[gjbwj8]

My 08 ford fusion (I-4) is having rough idle, particular when it starts in cold, go high 15k rpm  then back to below 1k rpm, after you switch gear, say on R, it is getting better quickly, most of time it will stabilize 700~800 rpm; During driving, when it stops on traffic, idle is set ~700 rpm with clear vibration; when it stops and gear switch to P, sometimes rough idle happen again, not like starting, idle could go lower than 500 rpm, then go up. I am wondering what cause this, vaccum leak? if so, how can I check, is it easy to fixed?

I had put in new spark plugs and cover gasket, it is an old car, but only has 113k on it, I am intending to keep another 2 years. Any help will be appreciated, thank you !