So there's this new type of metamagic called Familiar Spell
You can imbue your familiar with a spell.
Prerequisites: Spellcaster with familiar class feature.
Benefit: You can transfer a prepared spell to your familiar, allowing the familiar to cast that spell at a later time. Variables that rely on caster level function according to your caster level, not your familiar's Hit Dice, though your familiar's Intelligence may influence how precisely it can follow your instructions on how to use these spells.
Your familiar must be able to speak to cast spells with a verbal component (the ability to speak with its master or creatures of its kind is insufficient). Your familiar must be carrying any material or focus components necessary, unless the materials cost less than 1 gp and the spell is prepared with Eschew Materials. Attack rolls use your familiar's ability scores. A familiar spell counts against the number of spells you may prepare for as long as your familiar retains the spell. Once your familiar casts a retained spell, you can prepare a new spell in that slot the next time you prepare spells.
A familiar spell uses up a spell slot 3 levels higher than the spell's actual level. Your familiar can store a number of spell levels (including this modifier) equal to your caster level, but no spell's adjusted level can exceed half your caster level.
Special: If you are a spontaneous caster, you must select a specific spell with which to imbue your familiar; you cannot imbue your familiar with an open spell slot.
So this brings up some interesting questions.
First, how do feats apply to spellcasting? Since the familiar is the one who actually ends up casting the spell do feats like Spell Focus or Spell Specialization work?
Second, what happens when you cast a spell like Magic Jar modified by Familiar Spell? Does the familiar's soul take over creatures or does yours? What does this do to all of the abilities a Familiar has or grants? If your thrush familiar takes over the body of a green scorpion do you get a +3 bonus to Diplomacy, a +2 bonus to initiative, or nothing? Since the familiar's body is effectively dead while its soul is Magic Jarring does this disrupt or sever the familiar bond?
Third, is the familiar able to cast spells with a range of personal such as Mirror Image back on the caster?
When you disregard that part of the first line "allowing the familiar to cast that spell" as being fluff rather than crunch, then everything else points at the Master being the caster, not the Familiar.
So the effects of any feat the Master has that doesn't specifically apply at the moment of casting, can be transferred along with the spell.
The Familiar is still the origin of the spell when cast (hence the use of its Attack Bonus rather than its Master's), and so in the case of range:Personal spells I'd say they apply to the Familiar (like in your Magic Jar example) and cannot be cast by the Familiar on the Master (which is an effect applied when the spell is cast, and a Familiar does not have the Share Spells ability.
The above is all my personal idea though, and not backed by anything other than what I consider common sense.
(As for the "Jarred" familiar: I'd say the bonus granted remains the same. While not explicitly stated as such, it's some sort of magical or supernatural effect of the bond, and not a function of the Familiar's current body type.)