As shown in the picture I just want to make those 3 ends more round like a half circle maybe, but when I try to do that with Effect → Stylize → Round Corners it deforms/warps the whole object?
Select the nodes with the Direct Selection Tool and use the Live Corners Widget:
If your Illustrator version doesn't have Live Corners Widget, make your shape with paths, group them and from the Appearance Panel add two different stroke sizes and color with round caps:
It appears that the arcs are composed of only two nodes and when the rounding is performed, those nodes react in a manner inappropriate to your objective.
Have you considered to add a supporting node "inboard" of each of the corners? The extra points would maintain the existing arc structure and allow for the rounded corners.