In all of those cases the situation was more complicated than that and the Targaryens actions led to conflict at best and outright war at worst.
Maegor's usurpation of the throne did not go uncontested and he had to kill Aenys I's son Aegon. Everyone agreed that what Maegor did was unlawfull but nobody was about to object too loudly while he was alive.
Jaehaery I's cases is actually a good example of the limitations that the Targaryen kings faced when choosing their own successors. When his son Prince Aemon died he appointed his second son Baelon as heir instead of Aemon's daughter Rhaenys because unlike Viserys I later on, Jaehaerys knew damn well that the bulk of the lords of the realm would not be OK with woman ruling in her own right.
This one is actually completely wrong, as Jaehaerys didn't make this call. After Prince Baelon died Jaehaerys called a Great Council, and it was the assembled lords of the realm who decided to pass over Rhaenys' son in favor of Baelon's son.
This one is actually the preeminent example of how the Targaryens couldn't get away with the "do what I want because I'm the king and I say so" policy of inheritance. Viserys I was pretty damn clear about who he wanted to succeed him and the realm went to war before he was even cold on his bed over the issue.
We may be able to account for that with the fact that it is not actually a lake, it's a river, the Blackwater Rush.
Remember that before the battle Randyll Tarly came to tell Jaime that he wanted the army to be across the river as soon as possible. I think we are meant to assume that Bronn and Jaime were carried downstream by the current.
I would pity the poor soul who would have to do an entire show with the prosthesis and makeup necessary to play Glotka.
That's not true, actually. Robert did have a claim to the Iron Throne by blood.
Remember that Robert's grandmother was Rhaelle Targaryen, daughter of King Aegon V and sister to King Jaehaerys II. This made Aerys II and Steffon Baratheon (Robert's father) first cousins, and Robert himself, Rhaegar's second cousin.
That means that after the Tragedy of Summerhall, Robert, Stannis and Renly were the closest living relatives the royal family had. If some plague had killed Aerys and all his children and grandchildren, Robert would've inherited the Iron Throne as the eldest surviving male descendant of Aegon V.