Using 'I' there is correct, but it has gone out of usage. Now it sounds very formal or literary. In this context, it is a lot more natural to say 'me'.

Yes, it's fine. It sounds a little literary, but it is quite common. You could consider it to have an unwritten 'have' on the end, if that helps to understand the grammar.

Good to know, Ahmed.

Very helpful point. Thanks, Arasp.

It depends, If you see I and nothing after that it has a subjective meaning but you can guess the meaning of the rest of the sentence. When we use me, it is completely objective, and there is no hidden meaning after that. For example, in some cases you may hear this sentence: You just work exactly as I . ( It means: You just work exactly as I do or as I work) We can also use this structure: You just work exactly like me. The meanings of both sentences are the same but they are written in two different structures.