How to get rid of caterpillars without hurting lady bugs?

Hi,
Today I found the leaves of my adenium plants are being chewed and so I find for caterpillars and finally found the 4-5 very tiny catepillars and I hand picked them and killed them. At first, I plan to spray some cypermetrim so that when they chew the leaves, they will be all gone.

But the problem is at the same time, I found some little round bugs (I think and I hope them are Lady Bugs as I've never seen what a ladybug looks like in the real world). They are the size of the tip of a match. Are these little colourful bugs "The Lady Bugs"?

So, I want to know whether I can control caterpilllars without hurting these bugs if they really are lady bugs. The next question is that 2-3 days before I found out these caterpillars, I found some small green eggs on the leaves and at that time, I thought these can be the eggs of beneficial bugs and I leave them. So, I want to know whether these eggs are of Lady Bugs or of caterpillars.

If I can find some little caterpillars, does it mean that the big parents of them are also present around and hiding???? There are only 10 pots on my roof-top and no other plants and no ground contact and so, I'm thinking where these nasty caterpillars come from.

Thanks Again,
HK77

 

Consider BtK.

 

there is another post here that has some different pictures of lady "bugs' beetles, perhaps try a search with "lady beetles" as the keyword.
without a picture of either the caterpillars or the lady bugs, it's hard to determine what they may be.
I have attached pictures of the lady beetle, the eggs, and the larvae, often called "dragons" these dragons eat twice as many harmful insects as they do when fully developed.
The eggs, can very from a white, to a yellowish color, I have never seen them green, nor can I find reference to them being green
I would stick with the hand picking of these caterpillars, unless you have many plants

 

Some People says caterpillars hide during day time and emerge at night time to destroy the plants. Hiding means "between leaves or branches" or "dig into soil and hide in some deep place"? If they just hide between leaves and brancehse, it's not so difficult to hand pick one by one and kill them.

Thanks,
HK77