I used iso 800 on my nikon d5300. Pictures were too grainy. Used kit lens wide open?

Is this normal with a crop sensor camera?

does the lens affected the iso capability of a sensor?

does the kit lens fail as iso goes higher? Sharpness go down?

The higher the ISO, the grainier the pictures taken. That's just how cameras work. Many recommend staying under ISO400. Typical ISO rating are about 125.

The higher you go, the lower light you can take pictures in, but, the grain really begins to show.

ISO 800 will always give you a grainier picture.
Using any lens wide-open (big aperture/low 'f' number) will always give you inferior results to a smaller aperture. That is a generalisation but probably all you need to know, based on the wording of your question.
If the camera offers fully automated picture taking, I would be inclined to use that until you understand more about sensitivity and exposure control.

"Too grainy" is very subjective - if you re used to shooting in brilliant sunlight at ISO 80, almost any noise is going to be too much. The D5300 s low light performance is OK, but (for the same number of pixels) a smaller sensor means smaller pixels and a worse signal to noise (S/N) ratio. The lens itself (the glass) doesn't affect the amount of noise, but the smaller aperture of the kit lens might force you to use higher ISO values and hence you get a worse S/N ratio i.e. A noisier image.