-  for the last one year

The sentence is in the present perfect tense, which is used to describe actions that began in the past and continue up to the present. In this case, the action is "learning Tamil."

Here are the grammatical rules related to the sentence and the parts of the sentence:

1. The sentence is in the present perfect tense.
2. The sentence has a prepositional phrase "for the last one year" to show the duration of the action.
3. The sentence uses the word "but" to indicate a contrast between the action and the result.
4. The sentence has a noun phrase "no improvement whatsoever" to show the lack of progress.

The error is in part (2) because it uses the phrase "for last one year" instead of "for the last year." Here are the explanations of the rules and the correction:

1. The present perfect tense requires the use of the auxiliary verb "have" or "has" with the past participle of the verb.
2. The preposition "for" is used to indicate the duration of the action. It should be followed by a time period starting with "the" such as "the last year."
3. The word "but" is used to show the contrast between the action and the result.
4. The noun phrase "no improvement whatsoever" shows the lack of progress.

So, the correct sentence is: "You have been learning Tamil for the last year but you show no improvement whatsoever."