My character is a fighter 2/shadowcaster 1/scout 1/ardent 1. He had his hand nibbled off so he is one-handed, but can use the stump to cast spells like dust arrow (from ToM, which is a super-natural ability). He also has an "off-hand" bite attack that does 1d4 damage.
I have a plan to do this:
Skirmish 2d6 (+2d6 Improved Skirmish) = 4d6
Psionic Shot + Improved Psionic Shot = 4d6
Dust arrow = 2d4
If I use dimension hop to trigger Skirmish, and shoot with two rays, then it will do 4d6 (Skirmish) + 4d6 (Skirmish) + 4d6 (Psionic Shot) + 2d4 + 2d4 = a maximum of 88 damage.
If you want a guy who shoots lasers, I suggest the standard class warlock from Complete Arcane. A typical human ardent 1/fighter 2/scout 1/shadowcaster 1 isn't very good at this. Here are some things that may've been overlooked.
The general feat Improved Skirmish (Complete Scoundrel 78) has as a prerequisite Skirmish +2d6/+1 AC. This makes it so the feat is normally only available to a creature that possesses at least 5 levels in the class scout. The epic feat Improved Skirmish (Complete Adventurer 192) also isn't typically available, for obvious reasons.
The general feat Improved Skirmish (Complete Scoundrel 78) requires the scout move at least 20 ft. before its benefit can be realized. The character's manifester level for the dimension hop power must be at least 4 to reach 20 ft.; his is 1.
The feat Greater Psionic Shot (Expanded Psionics Handbook 47) exists. It possesses as one of its prerequisites a base attack bonus of +5; this character's is +2. (Officially, there is no feat Improved Psionic Shot.)
As a level 1 shadowcaster, you can 3/day take a standard action to use the fundamental arrow of dusk (Tome of Magic 141). This is a supernatural ability, so no gestures are required and no attacks of opportunity are provoked… fortunately.
The arrow of dusk fundamental deals nonlethal damage, making it useless against, for example, undead and most constructs. (Ask the DM if the character can voluntarily suffer a −4 on the attack roll to deal normal damage instead; don't be surprised if it's a no—also see this question.)
Because it's a standard action to employ a fundamental, unless he can take a second standard action during his turn, the character will only be able to employ the arrow of dusk fundamental once per turn. (It doesn't matter whether or not the character also on the same turn takes a swift action to manifest the dimension hop power.)
The feat Psionic Shot (XPH 50) (and, by extension, the feat Greater Psionic Shot) causes only the next ranged attack the warrior makes to deal extra damage. Further, using the feat Psionic Shot et al. expends the warrior's psionic focus so the typical creature can benefit from the feat usually only once every other turn.
It's not clear if instantaneous travel (like with the dimension hop power) triggers skirmish. Ask the DM. This is, I think, the least contentious issue. (Also see this question.)
Combining natural attacks with attacks from manufactured weapon is a thing. To sum up, generally a creature on its turn takes a full-round action to make all of its available manufactured weapon attacks then on the same turn makes all of its available natural weapon attacks except those natural weapon attacks suffer a -5 penalty on their attack rolls and deal normal damage but only +½ the creature's Strength bonus. So, yeah, that rapier/bite combo is a thing, but hitting with it may be challenging.
The feat Psionic Shot (Expanded Psionics Handbook 50) also mandates the feat Point Blank Shot (Player's Handbook 98). A typical human at character level 5 has 2 feats at level 1 and a feat at level 3; two levels of fighter grant 2 fighter bonus feats. Thus the character's spent 4 of his 5 available feats—a significant investment!—if the DM has ruled that the PC can take them at all. Also, keep in mind that the typical character like this won't be able to take psionic feats until he takes the first level of ardent.