Minimum number of transcation in blocks one must include? Anybody as the miner can just include 1 transaction and mine 12.5 award transaction and nonce and although it may not speed up my process as (number of transaction +Award+ Nonce)=some Constant to be inside the sha256() === &lt; target

so it does not save any calculation ??
but valid or invalid depends upon minimum one ...or not
A block is required to have one or more transactions. The first transaction must be the coinbase. (This is the transaction that claims the reward.)

Removing transactions from your block will not save you mining time. (Note that it may make your block propagate faster, and it may be impossible to tell if a transaction is valid when SPV mining.)