1- When I add a specific member, the system prevents me from editing her profile and shows a message that sounds like "You have been identified as a spambot" despite there is no apparent reason for this.
CB has no such message. You've something installed doing that or maybe you've a custom blocking rule configured in CB AntiSpam doing it.
2- As in any other organization, membership lasts 1 year. In many profiles I enter the registration and expiry dates and when I go to the list of members bothe dates have been moved of 1 day ahead. I happens occsionally without any apparent logic or consistency.
Datetimes stored in the database are done so as UTC. Then on display they are offset to the user or the sites timezone. To turn off offset for a date field edit it within CB > Field Management and under parameters you can turn off offsetting.