New Owner Need Some Advice

It's hard to tell from a photo, but it looks to me like the gel coat is peeled up, but the underlying fiberglass isn't damaged. The fact that the bow eye itself isn't loose supports that thinking. If so, the damage is only cosmetic, not structural. I'd remove the eye, fill the damaged area with a good filler, paint it to match and replace the eye.

I suspect that line is the attachment point for the bitter end of the anchor line.

I like Marine Tex. It's available in gray or white. The white is a fair match to the white on most boats, and, if you mask off just the area you're repairing, you might be able to get by without painting it.

I have no experience with the products you mentioned.