Aligning to match bottom of object without moving everything to bottom

camid,

What happens if you ClickDrag over the left group and the half circle to select both, then Click the half circle again, then in the Align palette Vertical Align Bottom?

There are a few ways to duplicate and align. If you have Smart Guides turned on, you should see a purplish line when it's aligned. To turn on Smart Guides, go to View > Smart Guides and make sure Smart Guides is ticked.

You could also Shift + select the other group so that you have both groups selected. In the Properties panel in the Align section, click the 3 dots for more options. In the lower right of the Align options, click Align To: and select Selection. Then click to align the bottoms.

One of my favorite ways to make a duplicate with symmetry is to select the part you want to be duplicated (you only need the original half), go to Effect > Distort & Transform > Transform... and at the bottom, set Copies to 1 and above that in Options, check Reflect X. You may need to change the registration point to get the reflection where you want.