Naval/ Fleet composition question(s)

[Atilius]

I doubt a wooden ship would towing another wooden ship.
Is that even possible with a ship that uses sails?

This was a common way of dealing with transports in the ancient world. Polybios (1.26) writes of the Romans at the Battle of Ecnomus:

Astern of the line which formed the base [of the triangular Roman formation] sailed the horse-transports, which were attached by tow-ropes to the ships of the third squadron.

Probably the biggest naval battle in the Mediterranean in the 3rd century BCE. 350 warships for a total of 700 ships doesn't seem that many...and really can't qualify for the largest naval battle.
...
Salamis 200 years earlier involved way more ships and more personnel.

Did you even read that article?

It says:

The candidates

• Salamis, September (28?) 480 BC. 371 Greek ships defeated 1,271 Persian ships in this decisive battle. Greek triremes had a crew of about 200 while their small penteconters had 50 oarsmen. With 1,642 ships altogether, it is thought possible that 200,000 sailors, soldiers and marines took part.
  
• Cape Ecnomus, (exact date and duration unknown) 256 BC. Like Salamis, Ecnomus was also a single engagement where 680 ships were fighting in a very small area. Some historians accept Roman claims that Rome had about 100,000 personnel. If this were true, which is unlikely, it would make it probable that at least 200,000 Roman and Carthaginian sailors and soldiers were involved.

The fact is we really have no accurate estimate of the total numbers of ships and men involved
in those two sea battles. Polybios says a total of 290,000 fought at Ecnomus; this has been
widely doubted. The numbers of ships at Salamis is constantly argued over. But it is certain that
both Salamis and Ecnomus were two of history's great naval battles.