Solarians with the Stellar Rush ability make a charge without the penalties as a standard action. My two questions here being, would that include the movement penalties, effectively allowing you to charge and spear someone 5 feet from you or around a tree? And my second being, now that it is a standard action, would I be able to use it as a full attack and hit 2-3 more people around the field? If so, it would allow you to run at 6 times your speed while still attacking three times each round to hit anyone you wanted (although provoking attacks of opportunity if the enemies aren't dealt with on each hit).
The only penalties associated with charge are -2 to AC, and -2 to the attack roll. Movement restrictions aren't penalties thus aren't ignored.
You could use your move action to move you character to a position where a charge is a legal action then use standard action to preform the stellar rush.
No you can't combine stellar rush with a full attack. Making a stellar rush uses your standard action for the turn. Since you no longer have a Swift, Move, and Standard action remaining after making a stellar rush you can't make a full attack. Or if you full attack first, you don't have a standard action remaining to make a stellar rush.
The restriction on a charge aren't penalties.
The penalties are as already noted the penalties to AC and attack rolls.
And no, you couldn't use stellar rush multiple times in a round or to make a full attack, as Maezer outlines you've used your standard action so you don't have the required actions remaining to make a full attack.