While in such situation, I never thought about the second point related to having bad opinion about another Muslim, as you mentioned.

I will InshAllah be more careful in this regard now.

I have a question in this regard, what should we do when a professional beggar asks for help? And that professional beggar is clearly visible to be not deserving.

You are correct it is not correct to give charity to professional beggars.
However, there should be enough proof of this or ortherwise there is another sin attached to this ,i.e. of having bad opinion (badgumani).
In questionalbe situation it is best to either give a very small amount or excuse your self humbly, without making any judgement.