I'll go through your questions one by one.
1.Why ReLU is used only on hidden layers specifically?
It's not necessarily used on hidden states only. ReLU work much better than "older" activation functions (such as Sigmoid and Tanh) because they backpropagate the error much better than their counterparts. All the most powerful activation functions are ReLU or some version of ReLU.
The typical ML tasks (classification and regression) do not require ReLU activation at the output layer, because of the nature of the task itself. However, sometimes regression do in fact require ReLU's. Let me make an example: I once trained an RNN to predict pollution levels, based on data from the last 24 hours. Since pollution levels cannot, by definition, go below zero, I used ReLU as the activation output for my regressor. In this way, you force your model to never go below zero with its prediction. House price prediction is another example in which you can use ReLU's at the output layers.
2.Why Sigmoid is a not used in Multi-class classification?
You need Softmax, because that returns a vector in which the activation of the final nodes sums up to one. In this way, you can explain each coeffient as "the probability of belonging to class X". A typical Softmax output is something like:
[ 0.3 , 0.5 , 0.2 ]
If you use Sigmoid instead, all nodes would be independent from each other. You could get results like:
[ 0.9 , 0.9 , 0.9 ], or:
[ 0.1 , 0.1 , 0.1 ]
which doesn't make a lot of sense for a classifier, and it cannot be interpreted as a vector of probabilities.
(You can use Sigmoid in case of binary classification with a single output node, that's the only case in which it would work.)
3.Why we do not use any activation function in regression problems having all negative values?
Because, I think, there's no need to do it. I don't see any practical usefulness coming from it.
4.Why we use "average='micro'" while calculating performance metric in multi_class classification? Ex:- f1-score(y_pred,y_test,average='micro')
Unfortunately there is no rule of thumb here. You should try different metrics and pick the one that fits your task the best.