Is there a limit to sending emails through my @me.com email address?

Yes:

Limits on Sending Messages

iCloud has several safeguards to ensure that only iCloud members can send messages using the iCloud outgoing mail server. Among these safeguards are reasonable limitations on:

• The total number of messages you can send each day (200 messages)
• The number of recipients to whom you can send each day (1000 recipients)
• The maximum number of recipients per message (100 recipients)
• The size of incoming and outgoing messages (20 MB)

iCloud email has been designed primarily for personal use. Sending unsolicited bulk email messages through iCloud email servers is prohibited.

From: http://support.apple.com/kb/HT4863

short said, using iCloud is totally useless then for sending out newsletters or any other mailing list messages.

it is good enough for strictly private use, sending emails to a couple of friends and family members daily. Right?

The daily limitation ... I am confused is this CET time or Cupertino time???

THANK you!

PS: At least the emails are in sync ... compared to other ISP imap problems ... puuuhhh ... complicated ...