The accurate descriptions of the Ottoman Empire from the given options are:
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experienced frequent conflict with Safavid Shi'ites as Sunni Muslims - True. The Ottoman Empire, being predominantly Sunni Muslim, had significant conflicts with the Safavid Empire, which was Shi'ite, particularly over territorial and religious differences.
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included territory that is now part of Turkey, Greece, and Egypt at its height - True. At its height, the Ottoman Empire encompassed large areas of Southeast Europe, Western Asia, and North Africa, including present-day Turkey, Greece, and Egypt.
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founded by Osman in the thirteenth century - True. The Ottoman Empire was founded by Osman I around the year 1299, making this statement correct.
The following statements are incorrect:
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expanded through Africa and Asia but could not successfully invade Europe - This statement is inaccurate. The Ottoman Empire successfully expanded into Europe and controlled significant parts of it, including the Balkans and even besieging cities like Vienna.
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had a brief moment of glory before being conquered by Mongols - This statement is incorrect. The Ottomans were not conquered by the Mongols; instead, they rose to power in the wake of the decline of the Mongol influence in the region.
Therefore, the correct answers are the first three statements.