Surely epsilon2 = -Poisson's*epsilon1 when strained in the 1-direction?
Yes, some dry UD has a few weft fibres, though these are rarely carbon. Usually they're something cheaper and less stiff like polyester. They also tend to be quite bent compared with the 1-direction fibres, often weaving around each tow in the 1-direction. This will increase E2 and decrease epsilon2 a bit, but not usually much and the effect on a laminate is a) small, and b) not that important. It's just another number to get right.
Re BMI, it behaves very similarly to epoxy, apart from its higher Tg and usually a somewhat higher modulus for the basic resin (E is typially above 4000 MPa vs. in the 3000s for epoxy). This doesn't affect selection, as either you need the Tg or you don't pay the extra (BMIs are usually a fair bit more money than epoxies). The higher E can make the GIc look less attractive than the KIc implies, if looking at choosing a tougher resin. I don't know if GIc or KIc is more important for laminate behaviour with damage.
If prepreg, the resin with the T800 fibres might be Toray's own 3900 (or 3911 if it's the version they supply from France). This is interlayer toughened like a few others (including Hexcel's 8551-7 as used by GE for fan blades) and is very tough, with a QI compression after impact strength typically well above 300 MPa. However, it might be an old, relatively cheap resin like 914, making for a laminate which is somewhat wanting in the toughness department no matter how good the fiber is.
Can you tell us the name of the manufacturer of the 'VKU' material and what it is? Just curious.