Cropping is inevitable with stabilization and tracking. (Look up match-moving and camera tracking).
As far as loss of resolution is concerned, if the initial video had motion blur (which it will), it will lose resolution - it's hard to say whether that is a perception thing or an actual 'thing' without studying the footage. Consumer-grade algorithms try to 'compensate' using available camera data in the file, and this isn't always a good thing.
Add some sharpening if you must.
As far as intermediary codecs are concerned, I don't recommend them at all. You could perfectly stabilize in After Effects with native footage, edited natively in Premiere Pro. Test, and see.
Yes, cropping is inevitable with stab-tracking.
As for intermediate codecs, it depends. They can be extremely usefull or extremely useless. It just depends.
The profesional editors here, and specially the onces involved in cinema,
never edit with the native material. It's not a question of power, those guys have all the computer power available, but stability
There is no magical ultimate workflow,
However, the practise is to cut with a low-bitrate intermediate and relink or conform in the end.
but also, there are intermediate codecs with a high-bitrate that are suitable for editing and manipulations and don't stress the software. Specially when
the original material is highly compressed like AVCHD. No serious editor cuts in AVCHD, unless it's small volume, fast delivery.
A good old DNxHD and you're good to go from the beginning to the end.
And that's why the broadcast are also so crazy about the minimal specs, exchange material, metadatas etc... because they don't have time the cinema editors have and they don't want hassles.
But using native material for image manipulation, and specialy for heavy color correction, if the native material is not robust
it will only lead to problems at one point or another of the pipeline. Long volume editing, the same.
That's something Arri understands and why the Alexa in Prores configuration is so popular, because the adquisition and editing being the same, and robust, the workflow is
straightforward. You shoot already in a format that is suitable for post-production and can handle severe CC. No surprise.
And that has a cost, the price of the Alexa. Same, using intermediate in post has a cost: time, but most of the time it's worth.
Manufacturers have developped those for good reasons. If you're in Avid, you better cut in Avid Native media (not native support). If you're in Grass Valley, the same.
It's not a golden rule but it avoids lots of hassles.
Most editors have only a word in mind: stability. No fancy fast turnarrounds. No risk. Avid? dnxhd. Apple? prores. Grass Valley? Canopus HQ etc...
Also, if you cumulate layers and complex fx within an editor in for ex AVCHD, the software will be prone to freeze easily. With the use of an intermediate it does not.
Then it's only a question of conforming to the higher-disponible media.
Now, if people wants to do special fx with low bitrate 4:2:0 AVCHDs or so...well, as we say: swim at your own risk.
So the use of intermediate is a question to be answered by everybody's priorities according to several parameters, but certainly not accesory.