The one that makes the zig zag in the web is a nice little (big) garden spider Argiope aurantia. I seldom see my spiders, but I see the webs frequently. It is a friend and always welcome.
I've never heard of a spider killing a plant. Maybe it was eating whatever was killing your plant.

Spider mites are the killers. They tend to attack evergreens, and roses, and they require much stronger controls than most insects.

Spider mites are too small to see, but if you place a white piece of paper under the leaves and tap the leaves to see what falls off . . . if the little specs move, it might be spider mites. Repeated washing off of leaves usually will control them or get the predator mite from a place that sells beneficial insects to control them. You might have to buy the predator mites more than once since once they run out of food (the spider mites) they die. If the spider mites come back, then you'll need more predatory mites.

The white gooey stuff might be from a spittle bug. It looks like spit on the plants, but they do little harm other than the substance looks gross. It can be washed off with a hose.

Spiders usually don't do damage to plants, but are predators and eat the bugs that are damaging your plants.

Small, white and gooey substance sounds like an aphid but it seems kinda hot for them.
There are numerous pests that fold leaves....leaf rollers come to mind. If you want to stay organic and there are worms in those folded leaves, get some Bt and spray them.

I've had problems with a type of mealy bug, they leave a white fluffy cottony stuff. They can be pretty destructive. And it isn't too hot for them.

I have been infested with mealy bugs. They are having a hay day with my plants during this drought. They are whats killing my plants. If you see white fluffy sticky stuff at the leaf axis it might be those.

Mealy bugs and similiar types are hard to control and often require two types of control.

Believe it or not, Florida has a worse mealy bug problem than us. I think unusually warm winters increase the populations.

They have two infestation stages: Active-in which they seem to be all over the place and they move from plant to plant.

The second stage is the sucking stage. (My description here probably isn't quite accurate)

During the active stage, they can be controlled with systemic insecticides. If anyone has an organic alternative let me know. I tried Spinosad and it didn't help, so I used Bayer Systemic and that is what worked.

Once they settle down, they won't be moving and systemics won't do much good. At this point they need mechanical type of control, such as hosing them off. Dormant oils and soaps are the recommended control at this point, but I'm reluctant to use them in this hot weather.

I wonder if they jump from plant to plant looking for a host to finally settle on?

It seems like pyrancatha, burford holly and possibly red tip photina and wax leaf ligustrum are the host plants that they settle on. Once they are settled, they don't produce as much cottony stuff, however their damage will be apparent. Leaves will appear cholorotic, or discolored. Evidence of non moving insects such as small dots or flakes will be on the underside of the leaves.

I think I had mealy bugs on my pyracantha last winter. They were in the sucking stage. I tried oils and soap and didn't do any good. Then, I got out the hose, attached the trigger spray and gave it a high pressure hosing.

I did this about once week and my pyracantha rebounded fairly quickly.

(Sorry if I sound a little loopy. I just got back from a walk in this heat)

I'm with everyone else. Never heard of a spider that damaged or ate plants. I've been known to "steal" spiders and bring them home from people trying to kill them. There are literally hundreds of spiders in my yard & often in the house. Every morning I get hit in the face by at least one web that has been built across the deck or a path. I didn't go on the backdeck for almost a month because a banana spider had built a beautiful web across it. I kind of ducked under & sprayed the plants on the other side of her. Broke my heart when she disappeared.

Tally HO!

Pricklypear, thanks for the info on the mealy bugs. They do seem to have slowed down somewhat now that they have killed a lot of my plants, lol. Maybe I can keep them in check with the water sprays now.