Greece

It is not strange at all, and the driver has had every kind of passenger there is, plenty of them on their own. On the heat, Sounion sits on a headland with wind coming off the water, so 38 there is a different 38 to the middle of Athens where the stone throws it back at you all afternoon. Shade at the temple itself is more or less nothing. Wear a hat and long sleeves. Go for the last two hours before sunset rather than two in the afternoon and you get the light thrown in.

If it is the money, the KTEL bus goes down the coast road from the terminal at Pedion tou Areos and it is about seven euros. Takes two hours because it calls at every town on the way. I slept through both directions so I genuinely cannot tell you anything about the scenery, sorry. Oh, and dorms in Koukaki were about 22 a night last summer if you still need a bed.

On your second question, in that part of the world a half day generally means four to five hours door to door, and the full day version adds the coastal stops and the temple at sunset and has you back at your hotel somewhere around eight. I would ask for the return time to be written down at the point of booking. In my experience that saves a good deal of polite confusion later in the day, particularly where there is a dinner reservation involved.