That all sounds 'bout right. My oil temp and pressure runs pretty close to what you're seeing as well.
As for the start-up, I turn the key ON and listen for the pumps to come up to pressure - takes a couple seconds or so. On a cold start it will crank for 2-3 seconds before it fires.
Being a '90, the calibration is such that idle will zoom up to about 1900 ± for 3-4 seconds before dropping back down to settle at 850 (750, I believe, is 'normal', but my idle was bumped 100 rpm as part of the secondary port throttles (SPTs) being deleted.)
For what its worth, the calibration in my Ford F150 truck is such that it too has an 1800-ish idle upon a cold start-up. However, it stays there for 7-8 seconds before dropping back to normal, and it only does that when the water temp is below some set level. I guess that is SOP for some fuel injected motors - prolly keeps them from stalling on cold fire-up as well as building up some oil pressure(?)).
The LT5 ain't no gen-I SBC! So, like many of us that graduated from SBC hot-rodding, you'll soon begin to understand there isn't much about the way those old motors run that applies to the LT5's characteristics...and don't ya know that is a very good thing!!