1. The heat is shared between neighbor reactors. You have to turn on or off all of your reactors, not by one, because the heat is shared between them and all connected heat pipes. You can connect 2 lines of exchangers to one reactor and zero to its neighbor and they will balance.
2. Neighbor bonus really makes more heat (not changing cell usage time) so you need more exchangers.
3. Single steam pipe can take input from up to 12 heat exchangers.
1 single reactor can handle 4 exchangers as stated in wiki.
1x2 reactors are very inefficient so I gave up at tweaking them.
For 2x2 reactors the maximum I could reach was 52 exchangers working (7-8 in a line) which is ~13exchangers per reactor.

For 2x3 reactors the maximum I could reach was 83 exchangers working (8-9 in a line) which is ~14 exchangers per reactor. Interesting that extra neighbor bonus didn't add any significant effect.

For 2xN heat pipes allow to connect up to 18 working exchangers in line per reactor though I'm not sure how many of them will be really used (should be tested with different N, theoretically it's 16 for 2x100 and 15 for 2x10). According to #1 you can take an average number and use this length for each reactor, even at corners.
So 2xN beats them all, right? What do you think?
Also the values are a bit bigger than in the wiki https://wiki.factorio.com/Tutorial:Nuclear_power
Update
The current winner is 11-12 in a double-row + some "corners":
