if you want them to...sure. Imaginary creatures can do anything the author wants them to do.

They have been known to turn into bats.

The only vampires that can change shape are the ones shown on television. There are what is called real vampires which is a cult that will bite draw blood and drink a little. These are otherwise just confused humans. There are real vampire bats which are bats that feed on the blood of animals (mostly live stock) much like a leech.

Modern vampires can generally shape shift into gloomy nocturnal animals, such as bats, owls, wolves or even mist. I believe that, with the Christians infiltrating on everyone's beliefs, the vampire came by these abilities through Satan, who was said to roam the Earth as a cat, a dog, a wolf, a rat, a snake and even a horse. The vampire being forsaken by God could imitate this ability, and while some transform into animals more fitting to the legend, there are plenty of different kinds of transformation, including more "human" looking shapes than their original undead state. Depending on the legend, and its attributes, in which much needs be considered, such as the disposition of feeding and its rules. Older stories tell that a vampire turns into a mole to dig its way out of its grave at night, or even a moth, to introduce itself in people's homes, despite the whole invitation rule. This aspect may also be perpetrated by the idea of a doppelganger, an older concept than that of the modernized vampire, which in certain cultures is seen as a creature, usually a bad omen. Always feared and damned by all, whether it's a physical thing or an idea.

Yes, I believe they are able to turn into squares, circles...even the occasional rhombus.

it depends on what kind of vampire it is. some can mind read some can shapeshift and others can move things with their minds.

well some turn into bats if you call that shapeshifting

haha no, they can't.unless you call turning paler and fangs shapshifting lol.&& no they cannot turn into bats,that's just a myth from movies && books.

None turn into bats, can fly, can control minds (unless they have a gift) and NONE can shapeshift.