It is possible manually install new versions by downloading them online, but if your phone is really out of date, newer versions will probably fail or crash if you did that.
The play store knows what your phone is and only let's you install working versions of an app.
So to sum up. If your phone is up to date but the play store is being funky, yeah you can manually download updated versions online. Or just wait for the play store to update you.
If your phone is actually really out of date and the play store isn't letting you update. Manually updating will probably just give you a broken app.
