I have a question. If pre-cum comes out of the penis by an erection, does that make someone unclean? Does pre-cum contain semen or cum? Do they have to follow procedures as if they had an ejaculation of semen (bathing in water, etc.)?
The laws of uncleanness were a part of the Old Testament and the laws the Israelites lived under. Those laws came to an end with Christ's death on the cross. "For He Himself is our peace, who has made both one, and has broken down the middle wall of separation, having abolished in His flesh the enmity, that is, the law of commandments contained in ordinances, so as to create in Himself one new man from the two, thus making peace, and that He might reconcile them both to God in one body through the cross, thereby putting to death the enmity" (Ephesians 2:14-16). Jesus removed the Old Law so as to bring Jews and Gentiles together under the New Law.
So, we can talk about the laws of uncleanness and learn lessons from them, but you need to first understand that Christians don't live under them. So first see Uncleanness to learn what the laws of uncleanness in general were about.
"If any man has an emission of semen, then he shall wash all his body in water, and be unclean until evening. And any garment and any leather on which there is semen, it shall be washed with water, and be unclean until evening. Also, when a woman lies with a man, and there is an emission of semen, they shall bathe in water, and be unclean until evening" (Leviticus 15:16-18).
A man became unclean under the Law of Moses when he ejaculated semen. Have erections or dripping pre-cum would not count. It is true that pre-cum may contain traces of semen in it, but this would happen when a man is getting close to ejaculating and some of the semen drips from the ejaculatory duct. This, by the way, is why it is possible to get a woman pregnant without ejaculating because sperm could be present in the pre-cum as a guy gets close to ejaculating. Any ejaculation of semen, whether through sex or some other means, such as wet dreams or masturbating, would make a man unclean until the following evening.