Yes, the quoted claims are largely correct. Some of the Constitutional powers mentioned were less slavery-focused than the quote suggests, but they certainly could be used in the ways the quote describes.
Article One, section 9 of the Constitution deals with the admission of people into the states:
The Migration or Importation of such Persons as any of the States now existing shall think proper to admit, shall not be prohibited by the Congress prior to the Year one thousand eight hundred and eight, but a Tax or duty may be imposed on such Importation, not exceeding ten dollars for each Person.
Here, the Constitution prohibits Congress from passing laws prohibiting the 'Migration or Importation' of anyone prior to 1808, though they could tax such importation. On January 1, 1808 this clause became irrelevant, allowing Congress's Act Prohibiting Importation of Slaves to come into effect.
As for the ability to mobilize militias, that is in Article One, Section 8, clauses 15 and 16:
To provide for calling forth the militia to execute the laws of the union, suppress insurrections and repel invasions;
To provide for organizing, arming, and disciplining, the militia, and for governing such part of them as may be employed in the service of the United States, reserving to the states respectively, the appointment of the officers, and the authority of training the militia according to the discipline prescribed by Congress;
It doesn't say that the militias were for suppressing "insurrections by the enslaved" specifically, but Congress could mobilize militias to deal with them like any other type of insurrection.
Finally, Article Four, section 2, clause 3 dealt with returning escaped slaves:
No Person held to Service or Labour in one State, under the Laws thereof, escaping into another, shall, in Consequence of any Law or Regulation therein, be discharged from such Service or Labour, but shall be delivered up on Claim of the Party to whom such Service or Labour may be due.