I'll answer your last question first. He'd certainly have had the choice of killing Nevill at the first opportunity but doing such might risk him being suspected and he still wouldn't gain anything because June would have been the major benefactor. Much more convenient to plan it round an already emotionally unstable sister and make it look as if it was she who was responsible. It was well planned, but we don't always think about ALL "what ifs" and it was this which let him down. I DO believe he'd planned for everyone -other than Sheila- to be in bed. I certainly don't believe he'd anticipated what happened in the kitchen -another reason for the violence of the beating, perhaps? Even at the last, Nevill manages to foil him?- it MAY have thrown him off guard which MAY have been the reason for the first and botched shot at Sheila. I don't he was thinking straight, OR he simply had no concept of the deep love most mothers have for their children, because Sheila would never have chosen to take her life with her mother, rather than the children she adored.
Nevill's Will specified that after certain bequests, the main residue of his estate would go to Jeremy, so there was no advantage in killing Nevill after June. In fact, some people have said he would kill Nevill first to take out the main resistance. I haven't seen June's Will, so I don't know what it said.
Let's say that the plan went wrong, and Nevill wasn't killed or incapacitated in the bedroom. He went down to the kitchen for some reason and Jeremy followed him. Would Jeremy really be in such a rage that he beat Nevill rather than kill him straightaway in some kind of revenge?
I can't read anything into where Sheila would have shot herself.