1. If I should win the lottery, I will buy everything.

1-2. Should I win the lottery, I will buy everything.

2. If I were rich, I could buy Glalaxy 4.

2-2. Were I rich, I could buy Galaxy 4.

3. If I had studied harder, I would have got better grades.

3-2. Had I studied harder, I would have got/gotten better grades.

(-Inversion-Is each pair the same? Are the sentences all grammatical? In #3-2, do we have to use 'got' or 'gotten'?)

1. There is no such thing that a person "should" win a lottery. The meaning does not make sense.

2. Correct.

2-2. Number 2 is correct.

3/3-2. Both these sentences are correct, but use "gotten."

1. is correct. It may not sound right to some people because it's in the subjunctive.

The rest of Anonymous's comments are right.

1. The first pair of sentences is expressing a hypothetical situation using the conditional "if" clause. The first sentence is in the present tense ("should win") while the second sentence is in the future tense ("will buy"). Both sentences are grammatically correct, but the second one is more commonly used.

To answer the question "If I should win the lottery, I will buy everything," you can do the following steps:
1. Read the sentence and identify the conditional "if" clause: "If I should win the lottery"
2. Understand that the speaker is talking about a hypothetical situation where they win the lottery.
3. Identify the consequence of the condition: "I will buy everything." The speaker is expressing their intention to buy everything if they win the lottery.

1-2. The second pair of sentences is expressing a hypothetical situation using the subjunctive mood. In the subjunctive mood, "if" clauses are followed by the verb in the simple past form, and the main clause is written in the conditional mood. Both sentences are grammatically correct, but the second one is less commonly used in modern English.

To answer the question "If I were rich, I could buy Galaxy 4," you can do the following steps:
1. Read the sentence and identify the conditional "if" clause: "If I were rich"
2. Understand that the speaker is talking about a hypothetical situation where they are rich.
3. Identify the consequence of the condition: "I could buy Galaxy 4." The speaker is expressing their ability to buy Galaxy 4 if they were rich.

2-2. In the sentence "Were I rich, I could buy Galaxy 4," the past subjunctive form of the verb "to be" is used, which is "were" instead of "was." Although the use of "were" is more traditional, some speakers use "was" in informal communication. Both "were" and "was" are acceptable in this context.

3. In the sentence "If I had studied harder, I would have got better grades," the first conditional clause is written in the past perfect tense.

To answer the question "Had I studied harder, I would have got/gotten better grades," you can do the following steps:
1. Read the sentence and identify the conditional "if" clause: "Had I studied harder"
2. Understand that the speaker is talking about a hypothetical situation in the past.
3. Identify the consequence of the condition: "I would have got/gotten better grades." The speaker is expressing a hypothetical outcome that could have happened if they had studied harder.

3-2. The choice between "got" and "gotten" in this sentence depends on your dialect of English. In British English, "got" is more commonly used, while in American English, "gotten" is preferred. Both forms are grammatically correct in their respective dialects.