Wrong. Familiars acquired using the Find Familiar spell cannot attack. Familiars acquired because they bond with you (several are mentioned in the Monster Manual) can use all their natural abilities (but you can't see through their eyes).
This. Familiars obtained through the
find familiar spell (or, rather, the Pact of the Chain warlock familiar improvement) are not same as the critters from the MM with the familiar sidebar. That is, the use the same stat block as the critters they're posing as, but are actually just spirits taking the form of imps, quasits, pseudodragons or sprites. Even their types can be different (celestial imps, fey quasit, fiend pseudodragon, etc.), and you don't get the goodies (magic resistance, etc.).
Likewise, as you say, if a MM pseudodragon decides to become your familiar, you only get the benefits listed in the creature's stat block sidebars. And if the creature dies, it's dead. It was not called by the spell, so it can't be brought back by casting
find familiar again.
So... I'd suggest talking to the DM to decide which version of blink dog familiar could be available in the game. Do you want a
find familiar familiar, or a companion creature functioning as a familiar (similar to options available in the MM)?
I think a blink dog falls far outside the scope of the plain
find familiar spell, as per the PHB. I don't necessarily think it would be overpowered, especially at mid-to-high levels, but it opens up a can of worms. If a rogue can get a blink dog, what can a wizard get out of the spell.
If you just want a companion, it would be easy for the DM to work it in the game.