Yes it does support series recording. No freeview+/freesat+ pvr removes the schedule at the end of the series because the system does not have an end of series flag, so there is no way the stb can know it's the last episode. Most delete the schedule after it not being used for 13 weeks. This is the specified minimum time before series crids can be used again for a different series.
In my humble opinion no. For many the 5800 modulator is more usefull than the hdmi on 5810. It's pretty pointless fitting hdmi to a SD stb unless you are going to use a high performance scaler (ie better than the TV's) which would make it a very expensive item. It might be usefull if you have a el cheapo HD TV (Tesco special)