IME, tenor uke strings are usually (but not always) higher gauge than soprano/concert. Some suppliers provide the same gauge for all 3 sizes. It all depends on the exact formulation of the string material, since some string material is denser than others, allowing thinner gauge.
Yeah it does. Nylon strings actually hurt the tips of my fingers. I don't mean callouses not formed, but the tips of the bones get bruised! I had to relearn to only fret with the minimum amount of pressure needed to get clear notes. To not mash the strings down to the fretboard. (There was a very good tread about this a few months ago.) Just hard enough. It's one of the reasons some of us, [me] harp on about getting a good setup on your uke. Lowering the strings to make it easier to fret and barre chords helps a lot. You may lose a little volume but it's a tradeoff I gladly pay. Caveat: If the strings are lowered too much, you can get a buzz, and it can affect the intonation.
I play only fluorocarbons, even though the string tension is higher, because the strings bend easier. (And I actually prefer their sound.) A few strings come in Soft, Medium and Hard tensions. Most are produced in the medium range.
I have a hard time, too. I find that Fremont Clear on my concert and Fremont Blackline on my tenor are very easy for me to play. Especially the Clear on the concert, that takes almost no effort at all.