I'm not sure if there is an industry-wide agreed upon statistical meaning of "typical", but it is usually taken to mean just that -- this is what you should typically expect to see -- but it is by no means a guarantee. The "maximum" spec is the guaranteed number.
On page 2 of the SHT25 data sheet there are two tables, for Temp and RH. Here the typical accuracies for RH (+-1.8%) and temp (+-0.2C) are listed, but you are referred to the graphs below for maximum specs. There you can see they guarantee (the solid line) 2% on RH from 10-90% RH and it gets worse as you approach 0%RH and 100%RH. Same with temp -- the best accuracy is from 10C to 60C and is worse outside those limits.
I don't know how they sense temperature...probably not a thermistor...but that's only a guess. I think the SHT sensors have humidity measurement as a primary goal, so that probably drives the level of temperature accuracy they provide. Beyond that, you'd have to ask Sensirion.
I've not spent any time looking for a breakout that would work for the thermistor measurement. Something with a good ADC of at least 14-bit resolution (15-16 bits preferred) could perhaps be made to work. You would also want the ability to control power to the thermistor because with typical measurement current levels there will be self heating just due to that current; you want to turn the current on, take a quick measurement and turn it off again before much self-heating can occur.
Something like this
http://www.osengr.org/Projects/Load-Cell-Shield/Load-Cell-Shield.html could be re-purposed, but would require a tweak to allow the Vref supply to be turned off and on by Arduino. I'll think a bit on what other options there might be.
Today, you are stuck with either trying to design with all thru-hole components for easy assembly -- but more and more manufacturers are only offering SMT parts. The problem with having someone do a run of SMT boards is organizing it, getting payments, and all the hassles that go with that. That's well beyond what I have time for these days. SeeedStudio was claiming to offer something along those lines a while back but I never went back to see if they actually pulled it off...