Because you’re both on the same network. AIM is SUPPOSED to create a “direct connection” between both users, which cuts out any other servers. This means you’re using the LAN network, and your speed limit is that of your wireless (probably a G network, which is 58mbps).
This is an old thread, but yes, it is possible to detect if someone is invisible, assuming they are on AIM (not AOL).
If you have AIM 5.9.x (OldVersion.com), open an IM with the user you wish to check. Click file, click get file. If the error is “user not available”, they are actually offline. It if allows you to getfile them, or says “user does not support this function”, they are online, but have you blocked and/or are invisible.