Q1. Is (American style) Dating Allowed in Islam?

As Muslims we should try to answer questions that come up in our lives Islamically. The two main sources of Islam are: The Quran and the (authentic) Sunnah of our prophet (saw).

Quran 004.059
O ye who believe! Obey Allah, and obey the Messenger, and those charged with authority among you. If ye differ in anything among yourselves, refer it to Allah and His Messenger, if ye do believe in Allah and the Last Day: That is best, and most suitable for final determination.

In other words "refer it to Allah(swt) and His messenger" mean check with the Quran (the word of God) and authentic hadith.

In answer to your question:

Quran 24:31

And say to the believing women that they should lower their gaze and guard their modesty; that they should not display their beauty and ornaments except what (must ordinarily) appear thereof; that they should draw their veils over their bosoms and not display their beauty except to their husbands, their fathers, their husband's fathers, their sons, their husbands' sons, their brothers or their brothers' sons, or their sisters' sons, or their women, or the slaves whom their right hands possess, or male servants free of physical needs, or small children who have no sense of the shame of sex; and that they should not strike their feet in order to draw attention to their hidden ornaments. And O ye Believers! turn ye all together towards Allah, that ye may attain Bliss.

Quran 24:30

Say to the believing men that they should lower their gaze and guard their modesty: that will make for greater purity for them: And Allah is well acquainted with all that they do.

Sahih Bukhari 001.010.504
Narrated Ibn Mas'ud: A man kissed a woman (unlawfully) and then went to the Prophet and informed him. Allah revealed: And offer prayers perfectly At the two ends of the day And in some hours of the night (i.e. the five compulsory prayers). Verily! good deeds remove (annul) the evil deeds (small sins) (11.114). The man asked Allah's Apostle, "Is it for me?" He said, "It is for all my followers."

(Kissing a non-Mahram here is clearly discouraged.)