You can tell:
El pune borcanele într-o pungă = He puts the jars in a bag.
Why „într-o” instead of „în o”, you ask? Well, because it is officially a contraction of „în o”. I guess this is one of the idiosyncrasies of the Romanian language that you will just have to learn.
If you use only „în pungă”, „din pungă”, „pe pungă” .... (you get the idea), the noun is in fact always definite, even if there is no article in this case. You do have to use the article if there is also an adjective describing the noun: „în punga mea” = „in my bag”.
Hope this explanation helps.
Not fully. Geantă is for carrying personal items, and although the object itself is rather versatile, you wouldn't carry your jars of food in it. Perhaps the most popular use for geantă is purse, hence my previous assessment. However, there are some extra-uses, such as when you go to the gym you use "o geantă de sport" (the large type where you fit half the gym itself) or when you travel you use "o geantă de voiaj", or when you go to the beach you use "o geantă de plajă".