Well, I have been fiddling with the D90 for a few months now, still haven't made too much progress on the D90 manual from Amazon, but I am trying when I have time.

Can you experts tell me what I can do differently with these couple pictures?

I am still learning, so please be gentle...

 

I think they're great pics of your adorable son. I don't see any problems here.

How're you liking the 35 f/1.8?

 

I don't see anything wrong with either; they're great shots of a brilliant subject. The second shot, especially. Just keep doing what you're doing; though, if you're trying to improve, the camera's manual will have limited benefits.

It's incredibly old by now -- twenty years -- but John Hedgecoe's Complete Guide to Photography is an incredible book to look into. It was a gift from my dad way back when (amusingly, it was one of the early books I remember reading), and it's stayed with me ever since. A great foundation, if you will.

Amazon.com: John Hedgecoe's Complete Guide To Photography: A Step-by-Step Course from the World's Best-Selling Photographer (9780806984278): John Hedgecoe: Books

 

If you were to use a flash (shooting straight up, bouncing on the ceiling), the lighting would be more even and lighten up those darker areas in the background ... but it does make the camera that much bulkier and heavier to play with. Or just an off-camera flash.
Someone really pedantic could have a gripe with the shadow just under his head on his shirt ... but for candid shots I say it's totally acceptable.

Those were shot at f1.8 I assume (or whatever lowest aperture you have), maybe crank it up a notch of 2 if light allows (crank up up the ISO if you have to). You see (especially in the second pic) how narrow the "in focus" band is? His thumb, cheeks and top of the head are perfectly sharp, but his eyes and nose (closer to the camera) aren't perfectly sharp, because of the very low aperture.
Same in the first pic, but it doesn't deter so much from the pic because his eyes are in focus mostly..

The first shot is really adorable.