The reason you cannot take the bite evolution is that the subtype already has it. You can however take improved bite to increase the damage. The claw evolution requires arms which the aberrant subtype lacks. They get tentacles instead.
Both the base form and subtype give the eidolon specific abilities. There are often interactions between the base form and subtype so that different combinations give different abilities. If you had chosen bipedal for the basic type and aberrant for the subtype you would not have bite, but would have limbs arm, limbs legs and slam instead of bite, grab, and tentacles mass.
Tentacles do more damage than claws and deal both bludgeoning and slashing damage. So, in reality you already have what you need.
The Grab from the subtype only applies to the tentacle attack. If you want your bite to also have grab you will need to select it again for bite.
Unchained material was very incomplete and untested. Hopefully, you can work with your GM to choose some extra evolutions for your Aberrant base form and subtype. Frankly, I think adding subtypes onto the existing complications of base forms and evolutions was a very bad move. If anything, the eidolon should have been made simpler.
You can't actually have grab more than once. If an evolution can be taken multiple times it will say something like, "This evolution can be selected more than once."
Whatever attack you have chosen with the grab evolution is what decides the base damage of your grapple when you choose to do damage as part of maintaining your grapple. Constrict lets you deal that damage every successful grapple. Normally you can only choose that option when successfully maintaining your grapple: move, damage, pin, tie-up. So, you could move the target and deal damage with constrict or you can damage the target and deal damage with constrict and so on. Constrict also deals its damage on the first round of grapple, because it doesn't require maintaining the grapple like "move" or "damage" does.
I get that you want 2 grabs per round, but really you are better off to go hard on the one tentacle mass attack. Give it Reach and Improved Damage. Push and pull are also useful additions, but of lower priority than basics like going large.
Now for some last tips. Don't forget that you can just grapple something normally. Grab gives you the +4 to grapple no matter how you do it and you can generally grapple something bigger than you, even when you can't "grab" them. Your grapple CMB will very often have better chances to hit than your tentacle mass attack bonus. Also, you probably already knew this but the Dirty Fighting feat is your best pick. Your eidolon should have that at level 1 and improved grapple right after it.