safe mode question

Since the search options isn’t working correctly i will ask it in
a new topic.

question 1:
I using wordpress about a year and i love it.. Since 2 months i
have another isp and it’s running safe mode.. They say that wordpress
runs in safe mode, but many people have trouble running it on safe mode.
What’s the reason that some people have problems in safe mode and some don’t?

question 2:
I have an option for changing ownerrights on dir’s. When i change this from
‘you’ to ‘webserver’ i can run wordpress in safe mode , but when i
start an ftp client i don’t see any dir. So what is webserver and
why can;t i see files with the ftp-client.

question 3:
When i turn off safe mode, what security problems do i get and want
can i do to avoid this(with out turning safe mode on).

Already thanks for replying!
(please keep it simple, i’am designer not a developer ??