[3r3bus]

To see what's connected to your router have a look at the administration page which will be your ip address with .1 at the end instead of the last digit ie 192.168.1.1 there should be a devices button on there and will give you the option to kick them while you set up a strong wpa2 password

What chmod said. It's really important to have a strong password protected network in place.

In regards to the ip conflicts, make sure it's not another device (that you own) that's causing this problem.

How long has this been happening? If it's only been a day or so it may be your ISP experiencing issues. Regardless, carry out all suggestions listed here. If you still continue to have problems with your slow internet connection, check the problem with your ISP and ensure your router is in working order.

If the IP conflicts continue to happen after the password change etc, it's probably a device you own, I've seen this happen quite a bit.