The carpenter in your screenshot is working, but very, very slowly. A Redstone Engine is woefully underpowered for most Forestry machines, and for some machines doesn't even satisfy the minimum input requirements.
For the Carpenter you should use at least one Stirling Engine, though two will make it go at a more satisfying speed. For other machines (such as the Thermionic Fabricator) I've found that Combustion Engines or IC2-powered Electrical Engines give satisfying results. I have a battery of four Electricals in my factory basement right now that are overkill for most of my mid-game Buildcraft and Forestry needs.
How many solar panels you need is up to you. Even though Forestry farms drain a lot of power, they're A-OK with receiving very little, and in fact I'd recommend that because you get seriously diminishing returns if you power them fully.
The wheat farms especially, because it only has to harvest the crops and replant. Other farms have to do a lot more (such as harvest multi-blocks structures, replace soil blocks, gather loose items). The wheat grows on its own, and you're probably OK with the farm and harvester taking a bit to harvest and replant.
On Forestry easy mode, I'd say 1-2 MJ/t is enough between the two machines to keep things going, which means a single electrical engine (Choke upgrade or not). You don't have to alternate, a forked conductive pipe will do the trick. I recommend giving the electrical engine double its intake so it can run through the night (obviously you're gonna need a buffer like a BatBox as well). Maybe a bit more so it can cope with inclement weather.
Let's say you have that engine set up with Choke and Efficiency, which means 3 EU/t. Use 3 solar panels to have it running during the day, 6 and a buffer to have it run through the night as well, and maybe 7-8 if you don't want rain to slow it down too much. (Although day is a bit longer than night, so it should slowly build up a buffer even with 6 solar panels.)
Best Answer
Basically, what happens is that the Peat Bog and Turbary don't need the incredible amount of power produced and it goes back in the Combustion Engine. This causes it to overheat no matter how much coolant you have in the engine. One of the perks of using Redstone Energy Conduits from Thermal Expansion is that they will automatically dissipate unused MJ out of the pipe instead of ejecting it back into the engine. But, for low energy machines in the early game, you should most likely use Peat-Fired Engines once you get peat going (you could manually farm it if you need to).