Swapping out my front and rear derailleurs
Sora is a road groupset. Road front derailleurs are all bottom cable pull (I believe), your bike (and most mountain bikes) is top cable pull, so that is not going to be compatible.

I don't think swapping a derailleur within the Tourney range is going to make very much difference. You will probably get much more value out of having a bike repair shop adjust the derailleurs properly.

Currently the Shimano mountain groupset progression is Altus then Deore (between those two, Alivio and Altus were offered in the last few years as well). 

Upgraded components will work better. You have to decide if it's worth it for you. Bear in mind that Altus and Deore are 9-speed groupsets so you'll be replacing derailleurs, shifters, cassette, chain, cable and housing at the very least. Your rear wheel hub may also have an older style 'freewheel' system rather than a 'freehub' system, if so you will not be able to upgrade.

Often, with bikes at the cheaper end of the spectrum, upgrading components is not worth the hassle, and just getting a better bike is the preferable option.