I am going, b'Ezer Hash-m, to cite some sources which will enable us to approach these questions. (See also Mishpetei ha'Torah, by Rav Tzvi Shpitz, Yerushalayim, Bava Kama, Siman 2, who addresses your second question comprehensively.)

1) The Gemara in Bava Kama (beginning of 26b) states that a person is liable for damage committed as "Ones," where he was not responsible for his actions, in just the same way that he is liable for what he did with "Ratzon," deliberately.

According to this, it would appear that the driver who splashed water on the pedestrian, or the person who sat on the glasses on the bench and broke them, should have to pay, because even if one would say that he is not to blame for what he did, nevertheless the Gemara states that one is liable even for what one did as "Ones."

2) However, we will see that this is not so simple at all. Look at Tosfos later (27b, DH u'Shmuel) who tells us a very important rule. He writes that even though "Ones" is liable, "Ones Gamur" is not liable; if he was totally not to blame for what he did, he does not have to pay for the damage.

Tosfos cites a proof for his contention that there are different levels of "Ones" from the Talmud Yerushalmi (also cited by Tosfos earlier, 4a, DH Keivan), which states that one is liable for damage done in one's sleep only if the vessels were there before he went to sleep and then he lied down there and broke the vessels in his sleep. However, if he had already fallen asleep and then someone came along and placed vessels next to him and he subsequently broke them in his sleep, he does not have to pay.

3) Now let us look at the first Mishnah in the third chapter of Bava Kama (27a). If one placed a jug in the main street and somebody else came and tripped on it and broke it, he is exempt for the damage. The Gemara there (27b) asks, why is he exempt? He should have looked where he was going! The Gemara answers (according to Rebbi Aba in the name of Ula) that this is because people do not usually look exactly where they are going, and thus one is not expected to do so and cannot be held liable for not doing so.

4) However, the Gemara then reports that there were similar cases to the above one and Shmuel and Rava ruled that the person who damaged the jug had to pay. Rav Papa explained that the reason was because the jug was placed next to the oil-press. Since people have permission to place jugs in that spot, it follows that the passer-by should have looked where he was going. Rashi (DH d'Ho'il) explains that their custom was that sometimes jugs were placed next to the press.

5) According to the above sources, we may suggest answers to your questions. If the car was driving at a permitted speed and in a normal fashion, we learn from what we cited above (#3) in the name of Ula that he is not expected to look where there are pedestrians who might get splashed when he goes through a puddle.

6) In addition, we also have a way of approaching the question about the man who sat on the bench and broke the glasses. If the bench was in a public place and it is not an accepted thing to place glasses in such a place, then the person who sat on them would not have to pay.

Kol Tuv,

Dovid Bloom