Always helps if I actually include the photo!

Too much sun will manifest as completely yellow leaves but only the ones in direct contact with sunlight. Leaves shielded by other leaves or blooms will remain dark green, giving the bloom a kaleidoscope look. It is always hard to guess how long but less than 2 weeks would be my guess. I had a hydrangea develop this issue days after the Crape Myrtle that provided shade lost some branches in a hailstorm.

You could dig a hole in the Limelight's first spot, put them there pot and all and then move them in October to the other location. Or I would put them in a protected location after 2 weeks of sun the test location. They normally go dormant for me as early as mid-to-late November thru sometime in December. Oakleafs go dormant much later (I had one that never went to sleep last year).

They should do well in the pot in which they came jut not safe to put the pot in the hot sun. While you can leave them in it, plastic pots and others get hot and can damage the roots so feel free to switch them to another type of container in shade.

As a general rule, I never plant any shrubs starting in mid May because it gets too hot. I also try not to buy any plants but that does not work sometimes. Hee hee.

You can put them in the test location (hopefully not) but, a location with bright shade and little wind would be easier on them now. Unfortunately, the bright shade location would not help you determine if the area is too sunny. Oh well. I have a LL in full shade but it is bright shade. Keep an eye on the shrub in case it needs water. I hand water every other Sunday whenever the weather is at or above 100. And I try to maintain 3-4" of mulch past the drip line.

ABSOLUTELY NOT. Do not set pots out in sunny (or hot) areas the middle of hot days. This is a suicide maneuver with most plants, not just hydrangeas.

That reminds... my Mother is in a residential facility where they took out some small pines that died and they have been putting holly cuttings and some annuals in that place. Well, the zinnias appear to be doing fine but, lord, the holly cuttings died and they just put new holly cuttings who look like they will die soon too. They are in full sun, with daily 100-degree temps. I would not try to put cuttings there until Fall but hey, they are intent on getting them to grow there. Sigh. So give the hydrangea some TLC, let it skip the worst of transplant shock and the summer. When temps go down, you can put it back in that area.