My transmission worked in reverse only. No forward movement at all. I took the pan off today and there was this part in it (see picture). Does anybody know about transmissions and can tell me what it is / where it goes and if it could be the cause of the problem?

 

Yes, I know what that is. It's a shipping plug for the dipstick tube.

It is inserted in the dipstick hole in the case at the transmission plant. When the transmission is installed in the truck the dipstick is pushed into the case and the plug drops into the pan.

 

The first time I did a filter/fluid change 95 f150/03f150, I was shocked when I saw that. I went to the local tranny shop, and the owner said it isn't anything important, and threw it away. I was PI$$*D off that he threw it, and actually went back through his garbage, too get that plug. I wanted another opinion, so I went to the local Ford garage, and they told me it wasn't important, and threw it away. Later that week, the tran's guy and I were talking (family friend) and he explained it was a shipping plug.
I was a little wiser on my 03, and I think the plug is in my toolbox! LOL

 

Thats just the plug, your problems are much deeper then that. A rebuild is in your future.