regarding transaction size in a block In What are the minimum sizes for transactions and blocks in Bitcoin?

The first transaction is set to be 65 bytes long, due to coinbase requirements. What about the second one ? That can be 61 bytes long ? Also, does each transaction carry a counter ? How is that added to the byte count.
What about the second one ? That can be 61 bytes long ? 


Yes.


  Also, does each transaction carry a counter ?


No. There is a global counter in the block that is right after the block header. That counter is the number of transactions included in the block. It is not part of any transaction and its size does not affect the size of any transaction in the block (compared to when that transaction was unconfirmed and in the mempool).

The transactions come after that counter just listed one after another with no additional information separating them (transactions follow a specific format so it is trivial to know when one ends and the next starts).