I would leave the new bearing as it came , don't take anything off it.
Once everything cleaned up I would check the new spigot bearing slides on the gearbox first motion shaft easily with a little high temp. grease to test, before fitting it to the centre of the flywheel/crankshaft, they usually tap in gentle using a large socket or similar and a copper mallet. Then a little of the same grease on the splines and slide the clutch centre plate up and down that shaft so you know it is easy, before fitting clutch centre plate and pressure plate to flywheel being careful to align it correctly so gearbox can slide on easily.
Regarding the release bearing after cleaning up the ridges and damage on the part of the gearbox it slides on, providing it is fairly easy that should not need too much grease as it has a nylon centre I see from photo.
Where the clutch release arm pivots I would use the same grease on it's pivot points and also where the release bearing contacts the release arm.
If the spring is in place on the arm, with the bearing in it's correct position it should be possible to locate the end of the spring top and bottom into the locating holes in the new release bearing so that once it is in place you should be able to work the arm and the bearing should slide easily up and down the shaft.
Alignment is everything when fitting the gearbox, so when ready have the bolts handy and maybe a couple of long large philips screwdrivers that are a nice fit in the threads, so that when almost there, you can slide the screwdrivers in two opposite thread holes to help guide the gearbox on, it is essential that it is in line and no matter how tired you get, Do Not let The Gearbox Rest On the Clutch!!!!! As that is when damage occurs

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It will help if the engine is hanging in the optimum position and ideally two fit blokes to lift and guide the gearbox into place.
I have fitted many gearboxes on my own when much younger with vehicle on stands safely then lifting gearbox using my arms and legs whilst laying on my back, including Fiat Ducato and Iveco Daily etc. sadly not anymore.