To get at least 4 recordings, then you need either a box with 4 tuners or a box with FBC tuners
Boxes with 4 tuners dont seem to be made any more.....and FBC tuners require the correct LNB fitted to you satellite dish
A hard drive
The advantage of a FBC tuner is the typically offer the equivalent of 8 normal tuners and you only need one cable from your dish to the tuner.
7 day Epg is easy with various plugins
there is auto timers to do "series link"
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* Be able to watch the box output on another non smart TV in another room
* Be able to control the box from the other room
There is various ways to do this, either via android apps or another enigma2 box, either way you will require an addition to the not so smart TV
Check out the sponsor store, below is a box i would consider good for your requirements
https://www.world-of-satellite…us-uno-4k-se-fbc-dvb-s-s2
The second device for the other TV can be a cheap android or enigma2 device as a tuner will not be required on that