Mail mirroring

So I'm using POP mail with 10.4.11's Mail.  Today I thought 
(brainlessly) to try out something new.  I wanted to mirror my POP Inbox 
with my webmail Inbox for a backup.  Seemed like the option "Remove copy 
from server after retrieving a message" would facilitate that.  So I 
click the "Remove Now" button.  It wiped out my entire webmail inbox!  I 
thought it should have removed only the messages I had already removed.  
For example, say today I receive 100 emails.  I keep 5.  Once I've 
trimmed my POP Inbox down to 5, there should be 5 in my webmail Inbox.  
But no.  Then the idiots that designed the webmail opted for automatic 
Trash deletion upon logout.  So everything was wiped out.  Brilliant.  

Is this typical?  My ISP blamed the OS X Mail program but I have my 
doubts.  

On the same topic, if use IMAP, and move 5 of those 100 incoming 
messages (mentioned above) to a folder called "Urgent", would that new 
"Urgent" folder also be automatically created with the same contents on 
my webmail IMAP?  And can anyone recommend a free IMAP email provider?  
I don't need a gigantic email storage space.  Probably 100mb would 
suffice.