How to apply opacity to one clip without being effected by the opacity of other clips?
When you set Opacity on a clip in the timeline, you can set it for the entire clip, or you can set it using timing markers, which Premiere will then gradually adjust to each Opacity as per the timing you've set within the clip.

Double check in the Effect Controls panel that you haven't set timing markers on your Opacity changes - this would result in the effect you describe. If you've got timing markers set, toggle them off, and then just go to the start of each clip and set the opacity you want for the entire clip.

The following help page may provide further info if this is the issue:
https://helpx.adobe.com/au/premiere-pro/using/adding-navigating-setting-keyframes.html