That depends on what you mean by "mini tornado," as there is no real definition for the term. Some people apply the term to whirlwinds such as dust devils, which aren't really tornadoes. In that case, then no.
Sometimes, especially outside of the U.S. tornadoes with relatively narrow damage paths are referred to as "mini tornadoes," regardless of intensity. In that case, such a tornado may be able to lift up a cow depending on how intense it is.
One tornado in France in 2008, which some outlets called a "mini tornado" caused isolated F4 damage. Such a tornado could pick up cows and much larger objects.
No. It might be able to pick up a new-born calf, but not a cow.
Yes. A strong tornado in the range of EF2 to EF5 can pick up a bus or even a train.
They pick it up from the ground
Keep on eating up mini tornadoes
"I'll pick you up later."
Air in a tornado moves upward rapidly, sometimes taking objects with it.
No. Though a very strong tornado might cause it to collapse.
An EF0 tornado can't pick up much of anything, so probably not.
A cow is born.
Yes, a very strong tornado can sweep it off its foundation and reduce it to rubble.
Yes, though it would require a rather strong tornado, probably at least an EF3.
That is extremely difficult to estimate and would depend on the size and strength of the tornado and what there is to pick up. A large, violent tornado moving through a developed area might be carrying many thousands of small objects.