I think once the spell runs out any effects which aren't instantaneous will end. If you get the healing hex, damage will stay cured, if you damage someone with some other effect gained via paragon surge they'll stay damaged or dead, but even permanent effects like the scar hex will end.
As to other feats - spell specialization to get +2 caster levels with a spell perhaps. Lunging spell touch to deliver touch spells, cunning to gain a skill, ability focus with a hex to add +2 DC.
If you're planning to use this a lot you might consider taking a feat or two to act as useful prerequisites. e.g. Improved Unarmed Strike opens up a lot of options, as would Dirty Fighting, Combat Expertise, Combat Reflexes, Spell Focus, even Weapon Focus. Not unlike the way a brawler needs to think when planning for martial flexibility.
If you use Paragon Surge to gain the Extra Hex feat, you can use the hex granted by that feat freely in accordance with the usual rules as long as the Paragon Surge spell is in effect. The duration of the hex effect is set when you cast it, so losing the ability to cast a given hex should not interrupt that duration if it lasts longer than the Paragon Surge spell.