Widget trouble no more Links widget?

Hi, I just updated one site to 3.5.1 and started a new site with the current version.
I have two questions here.
1. Suddenly I’m having trouble with the widgets on the older site. I can’t grab them or move them. I tried adding some text to a text widget and the five widgets above it suddenly disappeared. I had to restore my site via backup to get them back. Is anyone else having these kinds of issues?

2. What happened to the Links widget?? It’s been available to use on every site I’ve worked on, but I don’t see an option for it on my new site (which only has the 3.5.1 version). Is there something comparable I can use?