If you could add some other pics of the plant from various angles, someone should recognize it. Then it should be much easier to ID the caterpillar, unless it's an indiscriminate pest-type muncher (like armyworm.) Desirable butterflies & other has-a-caterpillar-stage critters usually have a very narrow range of host plants for their caterpillars.
A web search of "Genus species butterfly host plant" should help you determine in a few minutes if your caterpillar and/or eggs are going to be a butterfly, or something else. (Substitute the words "Genus species" with the actual botanical name, once ID'd.)