First, formatting is good.
Second...
You cannot take Improved Familiar unless you have an arcane spellcaster level, which alchemists do not.
You can share extracts with it through the Share Spells familiar feature, but not in any other way. You can also share Mutagens in this way.
Depends on the definition of payload. They are diminuitive or small, so it better not be large.
They can use a mutagen but only via the Share Spells familiar feature.
They are still a seperate creature even while attached for the purposes of spells.
You cannot have a small familiar. It calls out Diminuitive or Tiny. Per RAW, it would remain that size even when you shrank to or beneath that size, which would look a bit silly. Houserule something.
You cannot transfer a spell cast from an item from yourself to the familiar. If the item provides a touch spell - such as a wand of cure light wounds - you could cast it on your familiar as if it were another creature. But wands and items that cast spells on you explicitly could not have their effects apply to your familiar.
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The Share Spells familiar feature essentially means that when you cast a spell with a target of "You" you can instead cast it on your familiar as a touch spell. For alchemists, this means that you can drink an extract with a target of "You" or drink a mutagen, then touch your familiar as a free action taken as part of the casting/drinking and apply the effects of the spell/extract/mutagen to your familiar instead of yourself. Note that per RAW, this doesn't work with extracts from spells that do not have a range of personal, which kinda gives the shaft to most of your list, but you can talk to your DM to houserule it.