Can I choose for a large import of photos not to go to My Photo Stream?

Is there a way I can remove these large import of old photos from my PhotoStream to get my new pics I take with my iPhone to sync properly and to resume my Photo Streams shared with others?

Are you using My Photo Stream or Shared Albums? This is a bit ambiguous.

These are the limits, when you are using Shared albums or My Photo Stream - there are limits on the total number of photos and limits to the upload rate, see this link: iCloud: Photo Stream limits

• If you uploaded too many photos at once, you have to wait a bit, before you can upload again.
• If you uploaded to many photos, delete a few.

The 1TB iCloud storage is not used for My Photo Stream or Shared albums. They are used for iCloud Drive and iCloud Photo Library.

Your answer is a bit ambiguous and did not directly answer my question. How long? Hours? Days? Weeks?

Did you read the link I posted?

How long you will have to wait will depend on which of the limits you exceeded.

For My Photo Stream:

These are the My Photo Stream upload limits:

• Uploads to My Photo Stream per hour: 1000 photos
• Uploads to My Photo Stream per day: 10,000 photos
• Uploads to My Photo Stream per month: 25,000 photos

If you exceeded the 10000 photos limit, you may have to wait a full day.

If you exceeded the 25000 photos monthly limit, you may have to wait up to a month.

Or did you exceed a limit for shared albums? The details for the shared albums are listed in the link above.