Is it possible to play an assassin that cast's spells?
In Pathfinder, yes. In Rolemaster there is a semi-spellusing class called the "Nightblade" that, while suffering from all the above-mentioned limitations of semi-spellusers, can be fairly awesome.
Is it possible to play Rolemaster without an alignment (Does RM have an alignment system?)?
RM does not have an alignment system per se
though the assumption is there that certain actions (human sacrifice, summoning demons, creating armies of zombies, etc.) are evil, and thus subject to various game-mechanic things.
Do you think an assassin/ spell-caster would work within a group dynamic?
Depends entirely on the group and the story being told.
I really do think RPG's can be fun but I am so sick and tired of being herded in a direction. Why can't each of us (Hal, Lindsay and Gil) play what we want regardless of what is "supposed" to be?
I get things like leveling up and race and class, but why can't a diverse group of adventurers work together, even if they have different agendas and goals?
Again, depends on the story. So far you've been playing a prewritten adventure that assumes the players are going to be interested in saving the world. In a story written for the group, anything goes, though in general having a group that is too
diverse (aka a "freakshow" group) is a recipe for the whole thing breaking down into disruptive party infighting (which the players will justify as "good roleplaying"--sometimes even correctly). Yes of course everyone at your table is too mature for that kind of shenanigans. Every table thinks they are too mature for that kind of shenanigans. Yet it nearly always happens.
Why this happens ranges from simple immaturity ("I want more attention, so I'm going to disrupt the group and the game-world so that I get it.") to slavish adherence to a character's persona (To quote Joanna in Dorkness Rising
, "I'm lawful-good. Am I obligated to kill him for that?"), but in all cases the effect is the same: it turns the game into a competitive endeavor rather than a cooperative one. That's actually a perfectly valid playstyle for a number of groups, but many of us are of the opinion that real life is competitive enough; when we seek to escape it for a few hours each week, let's try for that mission-oriented teamwork-ideal that doesn't really exist outside the military.