Question 1. The 'lifedrinker' ability for a magus blackblade states that the monster slain must be one half hit die of the magus level. Does this mean that at level 19 when the ability becomes available that it only works on 8 hd creatures or anything 8 hd and up?
Question 2. There is a racial ability for half-elves that lets them use a spell trigger or completion device as though they were one class level higher, what does this mean and how does it affect the use of those items?
Question 3. Does the summoner eidolon receive a d10 hit die at every level including 1st?
1. It works on creatures with 9 HD or more. The ability should say "equal to or greater" for that to be the case, but I'm fairly confident that's how it's meant to work, as it would be silly if it only works on creatures with exactly half HD.
2. This is primarily relevant for scrolls. When casting a spell from a scroll, you must make a caster level check if your caster level is lower than the scroll's caster level. This ability grants you a bonus for determining that.
3. No. The table for the Eidolon under the Summoner class specifies how many HD the Eidolon has at each of the Summoner's levels. It starts a 1 HD at the Summoner's 1st level, and ends up with 15 HD at the Summoner's 19th level. (Essentially, it has HD equal to a medium BAB progression.)