Can a company pay an employee both salary(192) and consultancy fees(194J) for the whole year?

In my opinion
There is no restriction placed w.r.t. payment of consultancy as well as salary to an employee. GST registration is required where the value of aggregate turnover exceeds Rs. 20 Lakhs. However services by an employee to its employer in relation to his employment is covered under schedule III and hence neither supply of goods nor supply of services.
Aggregate turnover includes all supplies made by taxable person whether on his own account or on behalf of his principal.
And hence in my opinion salary should not be considered while reckoning the aggregate turnover as it is not a supply.
In first case GST registration is not required as turnover is 12Lakhs only.
In second case registration is reqd if A.T exceeds 20 Lakhs. since it has not exceeded threshold reg not required.
in last case threshold exceeded and hence registration required.

Yes a company can pay subject to discretion of the employees contractuL obligation.

At the time of deducting TDS on Salary, other consultancy Income (less expenses) should be considered in Form No 16 & calculation of Total Tax.

Generally this does took place in the past Vut now its a common feature.