The tenses (past simple / present perfect) are correct in the context in which you use them above. As to your question: "Should the last time always be followed by past simple and in the last hundred years by present perfect?", the best answer is that they usually are, but there are contexts in which they are not:

• This may be the last time that we have heard her sing. (present perfect)

• In the last hundred years of the first millenium most people lived in mud huts. (past simple)

With all due respect to my fellow answerers, I think you would be better off investing in a good pedagogial grammar, such as Swan's Practical English Usage, or engaging an ESL teacher. The answers here, including mine, are probably more likely to lead to confusion than to enlightenment.

The tenses (past simple / present perfect) are correct in the context in which you use them above. As to your question: "Should the last time always be followed by past simple and in the last hundred years by present perfect?", the best answer is that they usually are, but there are contexts in which they are not:

• This may be the last time that we have heard her sing. (present perfect)

• In the last hundred years of the first millenium most people lived in mud huts. (past simple)

With all due respect to my fellow answerers, I think you would be better off investing in a good pedagogial grammar, such as Swan's Practical English Usage, or engaging an ESL teacher. The answers to your numerous open questions, including mine, are probably more likely to lead to confusion than to enlightenment.