Her familiar evolves into an improved version of it
The shape or form of a witch's familiar is not important for her class abilities. When you take Improved Familiar, your witch's familiar is replaced by a new familiar, retaining all abilities they previously had. Witches may take Improved Familiar normally as counting her witch levels as wizard levels to qualify for the feat, as clarified in this FAQ item. This also doesn't cost you additional money either, as clarified by the developers on this FAQ item.
Sorcerer/Wizard: Can I dismiss my familiar so I may select a new familiar?
This isn't addressed in the rules anywhere, but yes, you should be able to dismiss a familiar if you want to select a new one. However, you must still wait 1 week and pay 200 gp for the 8-hour ritual. Dismissing a familiar is ending a link between your soul and it, so it should probably take about an hour.
The exception to the above is if you take the Improved Familiar feat, which allows you to immediately replace your familiar with the new familiar, at no cost or time required (it is assumed this occurs during whatever preparations you make while leveling up).
Once dismissed, an animal familiar is just a normal animal of its type (a special familiar from the Improved Familiar feat reverts to a normal creature of its type). Whether or not it wants to remain with you is up to your GM and probably based on how you treated the creature while it was your familiar.
To clarify, a witch knows all spells that her familiar knows, just like a wizard knows all spells written in his spellbook. They just cannot prepare spells without the aid of their familiar/spellbook, because they probably lack some minor details that are vital for the spell to be memorized.
But it is unclear what happens to their spells
If you are worried that your "old" familiar will lose all known spells when you pick a new familiar, you will have to have a chat with your GM about how that really works. It is agreed that your familiar is merely a conduit to your patron, but what exactly are those patrons are left completely at GM's discretion. They are not even given names or anything longer than a phrase of description. Some GMs will say the familiar merely pass the knowledge from the patron to the witch (based on folklore), others that the familiar is a living spellbook for the witch, and thus, losing a familiar work similar to losing a spellbook (your spells are gone).
There are ways around this, such as creating backup scrolls for every spell you know so you can have your new familiar eat them and learn those spells again. Or getting yourself a Stone Familiar, which is a bit costly (6,000 gp), but will fix the problem completely, allowing your to backup all your spells in the item.
Personally, I would say that it is perfectly fine for your old familiar to teach the new familiar during the process of replacement, similar to one witch's familiar teaching another witch's familiar, as this hasn't happened abruptly (such as having your familiar killed) and there is no mention on how long it takes, or how it even works, to get an Improved Familiar.