Honestly, you're opening up a can of worms.
Very few mainstream new-ish TVs have physical hard drives inside anymore, so unless he bought a Loewe Concept or a B&O or he has one of the rare exceptions from a mass market brand then I would check very carefully whether it's a real disc drive or if they're just referring to recording on an external USB drive.
Even where a TV does have an internal drive, you'll often find that recordings are somewhat limited. TVs with just a Freeview tuner only are frequently restricted to recording the channel that is being displayed onscreen. e.g. if you're watching ITV-1 then you can't record the movie playing at the same time on Film 4.
Those TVs with both a terrestrial (Freeview = aerial) and satellite tuner (Freesat = dish) may be able to record from one tuner whilst the signal from the other tuner is being watched. However, that does mean that the TV needs a signal cable from a TV aerial and a suitable satellite dish LNB to accomplish that. Where one or the other signal is missing then you're back to single tuner mode with the example ITV-1/Film 4 restriction.
There are of course the odd exceptions to this rule. Those TVs with two sat connections are likely to support a "watch one, record another" feature. The same set might also feature dual Freeview (aerial) tuners. This only requires a single aerial socket input and a suitable aerial signal. The manual will tell you whether the set has dual Freeview tuners.
Overriding all this stuff about Freesat is the type of LNB required.
I haven't come across any TVs with a satellite input where the Sat tuner is compatible with a standard wideband LNB as used with Sky Q systems. None. Zilch. Zip. Nada.
If his TV does have a satellite tuner, then it's highly likely that this will be compatible with the older style Sky LNB. It won't work with a Sky Q LNB. You/he are either going to have to change the LNB, or buy a recorder that is compatible with it, or add a box of electronics for a few hundred quid that will take the Q LNB signal and make it look like a standard LNB signal.
Trying to pull new cables in someone else's installation where you don't know if they're plastered in, or clipped, or just run in a way that makes it impossible without breaking in to the wall can turn in to a huge nightmare. This is particularly the case where they're trying to save money and maybe you're trying to help them do that. These things have a way of biting you in the bum. Whenever you either promise or predict that something will be simple in these kinds of custom installations, that's when Sod's Law strikes.
Personally I would leave the TV and its HDMI cable in place. Your friend has already had a recorder box in the lounge, so replacing that with another recorder that keeps a lot of the functionality he has been used to with Sky will make it an easier transition. The recorder for upstairs either needs to be the same wideband compatible type (simplest solution, but the most costly), or the LNB needs changing to a hybrid with outputs for wideband to the lounge and legacy to the bedroom recorder. He'll then be free to chose a lower cost sat receiver/recorder. This is the lowest cost option but involves some manual work in changing the lump on the end of the satellite dish.
As for Wi-Fi, if he's using a wireless router supplied by his internet supplier then that could be a reason why coverage is patchy. He doesn't have to have their router. Aftermarket wireless routers from Netgear, Buffalo, Linksys, Asus, TP-Link and others will usually outperform an ISP-supplied router by a significant margin both in range and speed.
Wireless-only repeaters tend to lose some speed compared to the main router. Those using powerline tech have had a reputation for causing interference.
