The mathematics is spot on - The only part of this build that approaches complicated is the Variable power, which costs (7 base -4 flaws) = 3 per rank (32 ranks gives 96 points), and Removable 1 drops that by 20%, giving 76.8, rounding to 77. The character build itself, however, is fundamentally broken (and not just from being able to get 160 Power Points worth of powers out of 77).
As an initial note, I find that there is nothing wrong with the concept. The part about only changing when resurrecting is perhaps the least problematic part of the variable power - one of the key things to remember about the Immortality power is that
all accumulated Hero Points are lost upon resurrecting via this power, which affects this build twice.
Evil GM hat goes on to assess the character's weak points.
1) Variable has a Sustained Duration, so they will not have any powers (aside from the immortality) after being stunned (which includes being asleep, dying, entranced, or surprised) - the only thing keeping the character from dropping to PL1 under NPC rules is the high Charisma (and the math says that's a bad choice too). The character will need to be killed again to have any powers.
2) The power can only be used five times before having to be recharged (Which, in RAW, is at GM discretion or by use of a hero point - the recommendation is that at least an hour's rest is required to reset it). Any NPC who exploits point 1 can very quickly render this character useless. And, since being killed removes the Hero Points, unless part of that Luck advantage relates to recharging this power (via expanded luck rules)
3) Tiring fatigues the character unless the character spends a hero point. As noted, Hero Points are lost, so unless that luck advantage has points relating to the recover action, the character will either have no powers, or will have powers and be fatigued.
4) Improved Critical on Variable does not mean what the player thinks it means. Improved Critical should refer to a specific attack, so whenever they attack with the Variable power (rather than a power gained through the Variable Power), they get the benefit of the improved critical range.
OK, Evil GM hat off, helpful GM hat on to smooth out the problems.
In order to build this power sanely, one extra is needed, and
Extra: Increased Duration (+1/rank). This makes the Duration Continuous, which means the chosen powers last until the character chooses to change them.
Flaw: Limited (-1/Rank). Can only change when resurrected. This keeps the theme of the power (changing powers when resurrecting), and the loss of all accumulated Hero Points is, to my mind, an acceptable trade-off - even with the six second resurrection time.
Possible Flaw: Unreliable (5 uses) (-1/Rank). I'm not certain how Unreliable (5 uses) interacts with non-instant durations - it hasn't come up in my game. However, I'd be inclined to not allow this, and have it as a Complication on the character instead - that way they can get a Hero Point when you don't let them change the setting
Possible Flaw - Removable (20% cost break). This should only be used if the character's variable powers comes from something that can be physically removed with some effort. There is one caveat I would include here - if the Variable power is removable, the Immortality should probably be removable as well.
While this doesn't allow anywhere near as much power to be packed in (and I'm extremely wary when flaws bring Variable to 5 points per rank, let alone below it), it also negates the key weaknesses detailed above.
The other key recommendation is to include a baseline of Abilities - having them as Enhanced Abilities in Variable modes is more expensive (and, if the Variable power is negated, the character isn't totally useless).
Oh, and the Mental power setting? Connected and Contacts are already in the main list of advantages, and the minion should really be a summon instead.
