The only thing you need for an exciting test match is two good teams and a pitch that has something in it for both batsman and bowlers throughout the whole 5 days.
I don't like the thought of a free hit rule in tests. If a bowler is bowling well and tightly, creating pressure on the batsman, and happens to bowl a no-ball. As it stands, this is not a problem - a no ball can still be a tight ball, and pressure is maintained on the batsman. With a free hit, the next ball the batsman takes a huge slog at, probably gets a boundary, and all the pressure is gone. There are those who think cricket is already a batsman's game; this would only make matters worse.
I think your second and fourth are conflicting. Having 4 day tests would increase the number of draws, which I don't think is good for cricket. Some draws, in which it goes down to the wire as the fielding team searches desperately for the last wicket, can be hugely exciting. The draws which are boring are the ones that it is obvious well before the conclusion of the match, and 4 day tests would increase the number of these.
The removal of the possibility of draws from tests is, frankly, ridiculous. For a start, Duckworth Lewis (while I am a fan of it) can be contraversial and this would not help in tests. Secondly, it is a system designed for limited overs games and therefore places great emphasis on rn rate and wickets in hand, neither of which are anywhere near as important. What is much more important in tests than one dayers is which wickets are in hand - in a ODI, even if you have Pietersen in with the tail, he probably only has 15 or 20 overs to bat; in tests he can bat all day. I think test cricket would be far too complex to develop an alternative system for, and anyway the removal of draws commits a cirdinal sin IMO - it allows tests to be won by teams incapable of taking 20 opposition wickets.
Don't really see the point of day night tests. The difference in light between day and night would be likely to disadvantage teams in one way or another. A more sensible suggestion would be the use of floodlights at the end of a days play if bad light is preventing play, but this would be dependant on acceptable performance between the red ball and floodlights, which I am not sure about.
There are already fielding restrictions in place in tests; to prevent bodyline bowling. I can't think of any other useful restrictions that could be introduced but if you could suggest some specific examples and reasons for them I'd be happy to comment.