'No' is the simple answer. I suspect your grammar book was written by a non-native.
1. We only use the present simple for future events when we are talking about an item on a fixed schedule. For example, if you know that the man who cleans the windows in your office block regularly comes on the same two or three days every week, but you can't remember exactly which days, you might - at a pinch - check by asking 'Does he come tomorrow?'. But it's very unlikely. Even in that case, 'Is he coming tomorrow?' or 'Will he be coming tomorrow?' is more natural. In other situations, we could also say 'Is he going to come tomorrow?' or 'Will he come tomorrow?'
99.9% of the time, when non-natives use a present simple to talk about a future event, it is an incorrect usage. I suspect that this is the case here.
2. This is completely wrong. You cannot use 'should' in this way.
It should be 'He insisted that he was doing ...' or 'He insisted that he had been doing..'
Likewise, 'He insisted that he should be innocent' is incorrect. It should be 'He insisted that he was innocent'.
I can only presume that whoever devised these sentences is over-applying what they learnt about the subjunctive mood. What is this so-called grammar book, by the way, and who wrote it?