Can my opponent see where my ships are?
No. Your fleet lives only on the server and the client is sent nothing but what it has already uncovered. Not even open devtools will reveal a position.
Do I get another shot for a hit?
Yes. A hit lets you fire again until you miss. Sinking a ship ends your turn.
Can I place my ships myself?
No. Both fleets are placed randomly and fairly, so the game starts right away and nobody gains an edge from placement.
Can ships touch each other?
Not side by side, but corners may touch. Two ships never lie directly next to each other, but they can meet diagonally.