For Swiftkey yes you can edit the size of keys. There's 3 sizes. It defaults to small I think. I made mine Large. Or you can try Swiftkey Tablet on your phone. I'm actually using that because keys are bigger than on normal Swiftkey if I remember correctly. Plus it's only one purchase for both tablet and phone instead of two. And oh yeah, not sure if they removed old Swiftkey but make sure you are downloading the newest Swiftkey. I seem to remember that old Swiftkey and Swiftkey 3(or whatever the latest is) coexisted in the play store.
Prediction sucks at first but both Swiftkey and Swype learns as you use it more often. I actually now type faster with it, since any typo's I made, they usually have the word I was actually trying to type as one of the predictions. There's one month trials of either anyway, so there's no harm in trying. The double space for a period is disabled in Swiftkey by default since space enters a prediction. You have to enable it in Advanced Settings.
My sister preferred Perfect Keyboard. If I remember correctly it also had the double tap to get a period.