Hello @bpradeepkumar !
I’m not 100% sure that the mobile app supports the Q search bar yet. There is a previous post from this year for the mobile app to support Q.
As for your other points, if you are not getting expected behavior from the UI, I would recommend an AWS support ticket. Here are the steps to open a support case. If your company has someone who manages your AWS account, you might not have direct access to AWS Support and will need to raise an internal ticket to your IT team or whomever manages your AWS account. They should be able to open an AWS Support case on your behalf.