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The only ways to kinda guess leopard gecko age are length, weight, colors, and patterns. Since he no longer has his bands, he would be at least 10 months old, my guess is.

She's about 7 inches, but since she's female she would be a bit smaller than a male her age. My guess would be somewhere between 8-12 months based off of his size.

My youngest gecko is about 9-10 months old, and she sheds around every 3 weeks or so. He may be around 10-12 months or so? How long is he?

I never took mine to get a wellness checkup. I will only take them to a vet if I fear there's something wrong with them, and that's not very likely.

I use a vine in one of my terrariums, I would recommend ones with a suction cup. Amazon has some good options.
https://www.amazon.com/terrarium-vines/s?k=terrarium+vines

You should feed your gecko whatever time works best for you. I feed mine in the evening and they'll come out at night and eat when they're hungry. He may have just been curious about you. My geckos...

I use a heat mat and a ceramic heating lamp. I turn the lamp off when I go to bed and turn it on again when I wake up, and have the mat going 24/7

I have two leopard geckos, and a smallish dog. My lowest one is a few inches above her head level, and the most my dog will do is look at her. Other than that she leaves her alone and ignores her....

Ah, yes, he was shedding, but he looks like he's perfectly healthy.

Okay so leopard geckos store fat in their tails, is there any way you can get a picture of his full body? The tail should be as thick as it's neck, that's a quick hack to see if he's a healthy weight.