Regarding the apps for Android, if in doubt use Google to look at reviews and what others say. By obvious I mean it's most times pretty easy to see what is official e.g.

https://play.google.com/store/search...e&c=apps&hl=en

You see that the first three are made by Skype, while the rest have other developers. You can use google to see what others say about the apps and the developers.

Same with Antivirus (I personally haven't installed any on my moms tablet, since she does not do online shopping at all)

https://play.google.com/store/search...android&c=apps

You see free products from both Avira and AVG there, also TrustGo and then the various other lesser known.

There is no option for online shopping for groceries and similar, where I live, no I have absolutely no experience in that area.

I would recommend the Galaxy Note over the Galaxy Tab if you plan on using it a lot, although there is absolutely a price difference to be considered. If I was getting one for myself rather than my mom, I would have definitely ordered the Galaxy Note 10.1 2014 rather than Galaxy Tab 3.

BTW I had big trouble finding a protective casing with keyboard combo for the Tab 3, while it was easy to get one or the other separately. I ended up buying one unofficial Chinese no-name product made for the Galaxy Tab 2 (fake leather casing with bluetooth keyboard) and using a scalpel to cut the various needed holes for e.g. camera and buttons. Worked great.