1 - Looks like Virginia creeper (Parthenocissus quinquefolia)... I took the easy one :-)

Number two may be leadwort or hardy plumbago. Three looks like 4 o'clock to me.

I never can tell Virginia Creeper from poison ivy, so in your mom's boots, I'd look up images of both before I watered that thing LOL!

#2 looks like wild purslane to me.

Thanks everyone! Her concern was that it might be poison ivy but then she counted the leaves and confirmed that there are five not three. I did give her the rule of thumb leaves of three let it be! I wonder if it creeped over from her next-door neighbors yard, mom certainly never placing any Virginia creeper in her yard and I doubt she wants to keep it if it becomes invasive.

I will also pass on the notes for the other photos, the plants pictured are currently growing in our plot at the community garden which sits on an old residential field. I wonder if there were wildflowers there before the community garden was started?

Also, plant three has tiny yellow flowers on it. I thought 4 o'clock's were pink with larger flowers?

My 4 o'clocks are hot pink. I was wrong :-)

I have yellow four o' clocks in our yard:)

Four o'clocks come in yellow too, but they are not tiny.

Omar

These flowers are tiny. I have no clue what plants 3 and 4 are. We are letting 2-4 grow in the community garden bed for now; I'd hate to get rid of it only to find that it's something useful.

I told my mom I knew 2 wasn't a weed but I wasn't sure about the others. Then I told her I'd ask my gardening friends online and they would probably know!

Some solanacea related to chinese lanterns (#3 and #4)

IMO none of them look like a "weed, weed".

Omar

Lol, that's the same thought I had, Omar.

Neglected to mention that Virginia creeper is one of several common plants containing calcium oxalate which does irritate skin on some people. Believe it is in the sap, so casual surface contact should not be a problem as with poision ivy. But if pruning or pulling it out, might want to cover up if uncertain about your own sensitivity.

The leaves are different, I'm pretty sure it's not 4'oclock.

The plant #4 looks a bit like my ' Yesterday Today Tomorrow " plant. I'll post a picture of my plant so that you can compare and see if it looks the same.