1. There's no difference between them because '내' is abbreviation for '나의'.
For the sake of simplicity, '내' ended up being used in modern days, whereas '나의' used in only literature such as poem, not in everyday conversation.
2. Basically '지금' indicates the moment when the speaker says as in:
a. 너 지금 컴퓨터 쓸 수 있어(You can use a computer now)
b. 지금은 여름이야(now is summertime OR it's summertime)
(You can replace it with 'currently' or 'right now')
However, '이제' includes not only the meaning of '지금' but also a causal relationship between the past and present for example:
a. 지금까지는 틀렸는데, 이제는/지금부터는 맞을 거야(it wasn't true until now, but it will be true as of now/from now on)
b. 이제 봄이 왔다(This time comes spring)
Hope this helps ;-P