Yes. Throw the rule book out; there are no rules, and you can practise at any time. This is usually a cultural question: in some cultures women do not do certain things while menstruating, and if that is your culture you may want to honour it. But as far as the system of Reiki is concerned, it makes no difference.

Not weird at all; your partner probably loves that you practise, and if not they are missing out. The one thing to keep in mind is to keep romance and Reiki separate. A person receiving a treatment needs to feel completely safe, and the system of Reiki is not a sexual practice in any way; we do not touch private parts of the body.

When they need something you are not qualified to give. If a client needs to talk, refer them to a counsellor; unless you are one, do not give advice or tell people about themselves. If they have a medical condition, they should see a doctor. If they seem very depressed, give them a crisis line. You are a Reiki practitioner, and that is a great thing; you do not have to look after all of it.