However, on the TV the TV shows correctly show under Shows without the movies but under Movies the TV shows are shown again along with all the movies. Is this as it should be, I expected separation, or am I doing something incorrectly.
It is probably all as it should be out of the box, if you have not altered anything.
The way media items are categorised and displayed is completely configurable through the use of
views, and there is a default set of views supplied with the program. I don't knwo what the actual default for movies is so I can't say whether what you describe is correct or not.
However, if you don't like the way it is being displayed, you can easily change it! Go to Tools/Options/Media Network and go to Customise DLNA Views. Thre you will find rules to filter and sort. Have a look around there to try to learn how it's doing it, and you can also look on the Wiki and ask in these forums for help on how to interpret it and how to create views. I would think you'd need to add a Rule For File Display on the Movies level to exclude TV Shows, however they are identified in your tags.
Also, the FF and rewind do nothing off the TV remote but play and pause do, is this a limitation of DNLA.
On balance, I would say it's a limitation in your TV, but I don't know enough about your model of TV to be able to say so. The ability to fastforward and rewind is called Seek. Lots of devices don't handle Seek properly on certain types of media file. One situation in which Seek sometimes can't be used is when items are being transcoded on the fly. So have you got transcoding turned on in MC? Again, look in the DLNA settings and see what it's currently set as.