200 Camry LE, 77,000 miles. Rattling noise over bumps, car front end dives when breaks are applied hard, Car bounces a couple times when human oushes on front end

The rattle (noticed at times under hard acceleration) is the cause of gas shock on the upper part of the engine loosing charge, in-turn causing the engine mounts extra stress and thus metal vibrating/rattling together.
The knocking (over bumps, etc. if you have noted that) is caused by worn bushings, most likely worn sway bar end links (you will see the links looking at the undercarriage, on both sides, they are a little steel "bars" with threaded ends on a 90 deg angle held by bushings e.g. example of front sway bar links ).
I noticed these noises coming on (at various times) at about ~140,000km or ~67,000mi and drove the car as it was until ~300,000km when i sold it (as is). Annoying noises.... yes... did I turn up the radio and carry on driving this car, not "fixing" anything (and I mean not a single $ spent on it aside from maintenance) and then sell the car... yes. The choice is yours.

First,as you travel over a rough road that causes the rattle apply the brakes slightly,is the rattle gone now?If so it's loosely mounted brake pads and/or worn brake caliper mounting bolts/sliders.
Rattle still there with your foot on the brake?Then it's usually the sway bar links and/or sway bar bushings.
To check this sway bar noise,disconnect the sway bar links and tie the bar up/out of the way and try that same road.
No noise now? address sway bar bushings and/or links.
Still noise?Might be struts.
If someone tells you,.you have loose lower control arm bushings,have them show you the play in the bushings before you spend any $$$.

Probably not, but we can't say until it is identified.
A very common cause of this in Camrys is that the rear suspension anti-sway bar retainer bushings become worn. See p 95
http://www.turboninjas.com/camry/sa.pdf

If you think the noise is more to the front then maybe a ball joint is worn, possibly the rack end ball joint or tie rod end.
Jack the front wheel up on each side in turn, grab the wheel at each side and shake it back and forth as hard as you can. If you hear or feel looseness, the problem is in the steering, as above.
Then shake the wheel while holding it at top and bottom. If you feel looseness then, the problem is in the front suspension joints somewhere.
Repeat this on the other front wheel. Let it down on the ground, then bounce each front corner up and down as hard as you can (you might have to have a second person with you doing this). If you hear a clunk or feel excessive bounciness, it is the shock absorber strut making noises. When bouncing like this, the car should resist, and not keep bouncing when you let go.

check the sway bar links and mounting brackets, ball joints, tie rods, ect. . A cv joint (usually) will make noises on hard turns like in parking lots, on the gas.

jack one side of car enough to take the weight off the spring then,using a tyre iron see if there is any movement in the ball joints(DO NOT GET UNDER CAR,ITS HEAVY)also when back on level bounce car,each side of front end should localise the clunk.
noises are hard to diagnose from a distance.....
regards
geoff
england

check your break pads, and calipa. check your wheel balancing and alignment

it could be the sway bar end links making the noise

You might have to drive the car on ramps so you can lay down under the front of the car.Have some one bounce or push the front of the car down over and over as hard as they can while you lay under the front and look and listen. You might have a loose shock absorber or another front end part.
Wear safety glasses while under the car.

-it could be the sawy bar linkages
-but also check to see if the struts are leaking or that it looks damp
-but because you said it doesn't look like it bouncing when you hit a dip most likely it could be that the struts are dead
-check to see the cars ride hieght that would give you a clue

Could be the lower control are bushing, it apparently is an issue with that model year.  Big bucks (850 CDN$) to fix as the 'whole' front end needs to be partially dropped and both should be done at the same time.  A mechanic should be able to see if that is a problem while the car is on the hoist.  The mechanic should be able to point to the area or point where the contact is being made. Mine lasted till 100,000 km, I heard it on the second hand test drive ( at 90,00 km) and asked a buddy ( a Toyota Master Mechanic) about it and he made me aware of it; i bought the car anyways.