Yes, it is the longevity character 夀.
To tell if an item is old or of a certain period, a side view is necessary. Unfortunately, pictures taken from an angle above like this one do not show the actual shape, because the proportions look distorted.
The base and rims are all a bit dark. This is usually a sign that an item may be new, if it is just normal dirt, it should be possible to wash it off, at least partially.
The wave pattern on the foot is the only thing that might indeed Ming, but it can also be copied. The lid and foot shape might mean it is export. If it is, then Qing would be more likely
How big is this? If you check the inside and outside, is there a horizontal seam somewhere on the body? Period items would likely have a seam as ceramics were not thrown in one go, usually.
