Hi jeanaef
I would leave the internet connections well alone at the minute.
You need Radio Frequency (RF) leads for the set up you have. Whilst they are coaxial the term is usually used for mainly audio uses.
I would get a powered aerial splitter and the leads from AMAZON http://www.amazon.co.uk/Philex-27814HSG-6-Way-Signal-Booster/dp/B00DCVX2H2/ref=sr_1_17?ie=UTF8&qid=1... There are lots available. Also the leads are on here and they deliver to your door.
If you do go for a powered splitter most use Male to Male connectors.to the TV, DVD and TTBox, so you will need 2 Male to Male leads instead. I would get 3 as I'm not sure about the lead for wall socket to this unit and mine is behind equipment. Anyway they're only a couple of Pounds and it's always useful to have a spare.!!
Regarding the aerial leads you should already have all of them.
You have the wall socket to TTbox one,Male (M) to MALE (M). To connect the TTbox to the DVD it will be what is called Female or (F) to Male (M) lead and another F to M one for the DVD to TV. All of the handbooks say that a lead is included.
Amazon links Male to Female http://www.amazon.co.uk/s/ref=nb_sb_noss?url=search-alias%3Daps&field-keywords=aerial+leads+male+to+female&rh=i%3Aaps%2Ck%3Aaerial+leads+male+to+female
All of the above are freely available from most shops like Wilkinsons, Currys ETC. AVOID "POUND SHOP" AERIAL LEADS as the ones I have tried are not properly shielded so give VERY bad reception, they seem to be O.K. for HDMI and Scarts although obviously they can vary.
Keep me informed. Good luck There's lots of TV to record over Xmas !!!!