We have a special needs son who can't walk and we were able to push him in a stroller no problem!
I think both you and your one-year-old will have a great time and enjoy the beauty of the Sequoia trees.
Yes! The trail in stroller friendly, and if he's able to walk he could run around with no problem!
The loop could be pleasant with a 1-yr old. The meadows can be thick with mosquitos and gnats in spring. I don't think ticks are a concern at that elevation. The edges of that meadow will have some shade, but not as much as other trails in the Giant Forest. I'd probably skip the stroller if you've got an alternative like a tot backpack or sling-amajig.
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