Boars tamed relatively easy for me. Made a quick pen maybe 4x6, let two chase me in there threw like 40 mushrooms in there and checked back a bit later and it was tamed. Boars give you a leather farm, as they seem to have a greatly reduced chance to drop meat when tamed. (at least for me)

For tames to mate there must be enough room for the animals and the animals must be fed. As far as I can tell they do not starve. The above mentioned pen enabled my boars to grow to 5, sometimes 6 pigs. To test why they were capped I expanded the pen (rough estimate) by about 4x and threw some food it. By the next in game day there was 11. (the boars had stayed at 5/6 pigs for days of real time, with my friends leaving them alone)

I have not yet noticed any sort of a taming bar, but on my wolves they had a percentage in numbers that I had to get really close to see.

From what ive tried Boars will not eat; Honey/glow mushrooms. Will eat; Carrots, turnips, raspberries, blueberries, and redcaps