RAW spells only do what the spell description says. So, you can only use it to grapple other creatures. That's not to say your DM won't allow other more creative uses, but I personally wouldn't allow them to wield a weapon. For me, that's a little strong for a 1st level spell.
Also, with my reading of it, yes when the creature attacks or breaks the tendrils, the mage doesn't take any damage.
To me, this really just seems like a reflavoring of the spell Entangle and since both are 1st level, they should remain roughly the same strength. Its a minor control spell where you can keep someone where you want them.
Nowhere does it say the tongue is "prehensile" just that it can wrap around a limb. You could wrap it around a tree (it would automatically succeed the grapple check) and if you wanted to use it as a rope to climb or swing, the tongue has the same break DC as silk rope, so I can easily see that working.
For using the tongue to lift you up, the rope would have to make a Strength check, and the spell description only mentions it has an effective 20 strength for grappling and doesn't mention its strength for anything else.
Again look at the spell Animate Rope for ideas. It's another level 1 spell that is even more similar (except Tongue Tendrils supplies the rope automatically). Which doesn't mention anything about using the animated rope to lift just:
“coil” (form a neat, coiled stack), “coil and knot,” “loop,” “loop and knot,” “tie and knot,” and the opposites of all of the above
In my opinion, when looking to maximize the utility of a single spell, I think it makes sense to look at (or at least think about) what other spells of the same level can do. If a spell of the same level can do it explicitly but has limitations (needs pre-existing plant material or a rope) that your new use of a spell would overcome, it's important that you understand those limitations.
Also it's important to note, that all of the suggestions for rules here are not RAW as far as I'm aware, just how I would rule it if I were the DM.