A peruta is a copper coin equivalent to approximately .2 grams of silver. At the current value of silver in the range of $17 per oz, a peruta would be worth $.007, less than one cent. HaRav Moshe Feinstein zatzal ruled that to be considered a peruta value an item must have purchasing power, and ruled that a nickel is the minimum that qualifies.

If she is currently not married it is neither necessary nor appropriate for her to go to the mikva.

You are correct that there are two opinions. The Rash on the Mishnayos writes that chanata is the beginning of the formation of the fruit while Tosafos and the Rambam rule that it is 1/3 of the fruit's growth. Shulchan Aruch follows the second opinion which is the accepted Halacha. In most years none of the shesek fruits reach 1/3 of their development before Tu b'Shvat and Harav Elyashiv shlita paskens that one need not suspect otherwise. However if one knows that some of the fruit on the tree reached chanata before Tu b'Shvat and others didn't and at the time of harvest they are indistinguishable there is a dilemma. the acceptable solutions are to either separate terumos and ma'aseros from each individual fruit separately or to find fruits from a different tree that has not yet had its terumos and ma'aseros taken yet and that are certainly from both years and to separate terumos and ma'aseros on the questionable tree from them.

Lemons are a separate issue and the Chazon Ish considers them to be a safek if their Halacha is similar to an esrog that follows the picking and not the chanata like most fruit.