How does dna of a plant produced using tissue culture compare to the dna of its parent plant? ?

All will be depend on your aims - what genome you interested in (nuclear, cp or mt) and what plants you work - live or extinct. But generally the next tisseus are prefered to use - apical and lateral meristems and live vegetative tissues. As for parts you may use buds, kambium, leaves, flowers, seeds and so on. For some studies pollen is also good to use.

Except aims of the research in case of choise tissue are some general critical factors: 1) tissue availability 2) quantity of integer DNA of genome you interested in this tissue 3) quantity of specific secondary metabolites which can affect to DNA isolation.

Another cruical moment - the choise of most suitable technique or kit for DNA isolation for your own aims.

"do a testcross with a homozygous recessive plant."