Page 52 of the PHB say that a familiar has half the HD and HP of their master. Is this the character's total level, or just of their relevant Arcane class level?
You use the total level and hit points as your base
The Player's Handbook glossary (p. 306) explains what "character level" means:
A character’s total level. For a character with levels in only one class, class level and character level are the same thing.
So it is the character's total level that factors in the calculation.
For the purpose of effects related to number of Hit Dice, use the master’s character level or the familiar’s normal HD total, whichever is higher.
There is no halving applied to HD for resolving effects.
The familiar has one-half the master’s total hit points (not including temporary hit points), rounded down, regardless of its actual Hit Dice.
Again you use the character's total hit points. These are halved, rounding down.