How long can Canadian citizens stay in the U.S. after TN visas expire?

There is no grace period for expired TN visa and you cannot stay in the country without status. Otherwise, your EB-5 petition will be negatively impacted. However, there are two visitor visa options: 1) as a Canadian you can re-enter the U.S. through the Visa Waiver Pilot (VWP), and you can stay in the US for 90 days; 2) alternatively, you can re-enter as a regular visitor (B1/B2) which allows you to stay for up to 180 days. In spite of these options, the question of whether your stay in the U.S. will be enough to allow the approval of your EB-5 petition and the filing of an application to adjust your status depends on the processing of your I-526 petition. Thus, leaving the U.S. and staying out in Canada may actually be beneficial. Advisedly, consult your EB-5 or any immigration attorney for further analysis of your options.

There is no grace period. You need to leave or change to another status. After 180 days you could trigger a bar when you leave.

I generally do not recommend re-entering as a visitor quickly after another non-immigrant status ends. An I-526 petition by itself may get you some extra questions about your intent for entering.

Yes, it might. That is why you should renew your TN before it expires and avoid becoming out-of-status. Since you have already declared your immigrant intent via the I-526 petition you have already filed, if you leave the U.S. before extending your TN status, you might be denied re-entry to the U.S. as a tourist. It will be hard to convince the officer on the border that you are entering for "touristic purposes", only and that you intend to return to Canada.

Best would be to renew the TN. To obtain a visitor status, the CBP officer must believe you intend to return home, which will be tough with an I-526 pending. But if set up for immigrant visa processing, this may work.

Upon the completion of your work in the U.S. under TN status, you have a reasonable time to either depart the U.S. or file to change employer or status within a reasonable time frame. Usually within 30 days. Sooner the better.

Better to file for an extension of your TN status and not to go out of status. It may be denied re-entry as a tourist on the grounds you are not bona fide visitors, as you intend to immigrate to the U.S.