I would like to know if the number of emails sent per minute and the email size are relevant for spam filters.
Usually big email provider will take precautions to defer your email if your sending rate was above normal. Abnormal sending rate is a sign of spam outbreak. This pattern usually caused by hijacked server then spammer will send spam as many as possible for very short time. For example, see this question about sending rate to Yahoo.
As for email size, I don't have data to support/reject your assumption (email size affect spam filters).
If they are relevant, are they related to the machine sender domain or the return path domain?
Usually spam filter will blacklist the client IP address, because return-path-domain was easily forged. With that blacklist, you, as server administrator, will know that destination server doesn't like either your email content or your sending rate.