1) See MS KB 152104 - "How to Prevent a Windows 95, Windows 98, or Windows
Me Logon Prompt at Startup" (http://support.microsoft.com?kbid=152104).

Basically you need to change to using Windows Logon in Control Panel |
Network. Then when you next log on don't enter a password (leave blank)
and click OK.  If you've already allocated a password, logon and then
delete or better rename the password file in the Windows folder - this is
a file whose name is your logon name with a pwl extension.

Don't click Cancel or Escape as this will mean that you don't log on and
are instead what is called the Default User which means you won't be able
to save passwords and have access to certain features.

2) You will only get a connection icon in Win Me is you are using DUN, for
example using a usb ADSL modem which uses Dial-Up Networking.  If however
you are connecting via a network adapter (NIC) to a router then you will
not see what you refer to as a connection icon.  There are some third
party tools which include this functionality including I seem to recall
DU-Meter.