I am buying a 2001 Ford F150 with a broken frame near rear leaf spring mounts. Can I still drive it like this?

Broken rear leaf spring, bad motor or transmission mount. Broken frame or brake proportionate valve.

Check your ball-joints. There are pros and cons to guessing different components. What I visualize is that you have low motion noise{slow approach to parking spot) and noise going over rough roads(no clutch, no braking).

There was a recall on some gas tank straps, which a rough road could reveal, but it would not affect going into a parking spot. Check rear leaf springs for cracked leafs. The truck body settles when parking and driving motion could make broken leaf spring chirp.

Check motor mounts. The exhaust pipes and joints in what is called the "donut" can chirp if the tailpipes are rigid and the engine moves on bad mounts. The donut becomes the only flexible connection in the exhaust system.

replace spring mounts- cut rivets out and replace mounts(use harden bolts) have rotten frame "fish plated" by welding shop

You're wasting both time and money on a vehicle that is not worth the $$ you would have to spend to repair it - if you can at all. Junkyard, dude. Sorry. I replaced the leaf springs and hangers on a '03 Silverado several years ago - $1,000. I did it because I only paid $2,500 for the truck, which was otherwise OK.

Both of my big Ford trucks had to have the rear leaf spring mounts replaced. Look at your rear springs - if they are leaf style then check the rear mount points to see if they have broken loose. The springs end up moving way too much and it is not safe.

a 10 year old car with a rusted frame? i would call ford and complain, but look in the yellow pages under welders,and see if one of them can fabricate you a piece and weld it on, so you can re-attach the leaf springs

Yes but you need two thumbs. Jack the truck and support it on the frame ahead of the axel so the axel can hang on its own weight. Remove the bolts and mount to the bad spring - remove the axel mount first, Let the axel sag and put something under the tire to help hold it. Remove the spring mount bolts to the frame and lower the spring out the rear. reinstall is the reverse --- BUT --- the new spring may not fit right in the spring mounts. Mount the front bolt first and then the rear - you may have to use a pry-bar and force the spring into the rear mount.

eaither tthe shoks are bad or you have a broken center spring bolt. of the leaf springs or the spring busings are wore out.

Do you have:
1. Shocks and Leaf Springs?
If so: the Shocks could be "shot" and/or broken or completely discharged. OR the Leaf Springs Retainers or the Leaf Springs have broken. The Retainers should have two (2) bolts holding braces which hold the multiple leafs of the Leaf Springs together. Check these. Also you have bushings bolted then welded to the frame that will need to be checked.
2. Struts with Coils (Springs)?
If so: the Struts could be "shot, and/or broken or completely discharged. The Coils (Springs) could be broken of dislocated.
3. Coils (Springs) without Struts?
If so: the Coils (Springs) could be broken or dislocated.
4. Independent Bar Suspension?
If so: the independent bars could be bent, broken or dislocated from their frame connections with the frame.
5. Solid Axle?
If so: the Axle could be bent, broken or dislocated from their frame connections with the frame.
Since you cannot lift the vehicle, I am assuming you are using the jack under the axle to lift? This would point to the Axle/Bars being broken.

Was an excessive load (weight) put on the back of the SUV lately?

If you can't lift the rear of the vehicle, jack-up and properly support the front then jack-up and support the middle towars the rear of the vehicle to gain access to the rear of the vehicle for a better look.
However while doing this if the rear starts rising: keep a careful eye on the rear tires to see if they are going lower than what they would normally go when you are jacking-up the rear, especially with a broken Axle or Bars. THIS COULD CAUSE THE BROKEN OR DISLOCATED PARTS TO FURTHER BREAK OR CAUSE OTHER CONNECTING PARTS TO FAIL AND BREAK OR COULD CAUSE DAMAGE TO THE REST OF THE SURROUNDING AREAS OF THE CAR. I have seen an Axle and Bars that were broken "pierce" into the body of the vehicle because they were not carefully watching.
Let me know if this helped, or if you have any additional information, problems, or questions. Feel free to contact me at FixYa.com!
ps...when describing your problem feel free to fully explain in as much detail as you can, including in this case what type of rear suspension system you have, 2WD, 4WD, AWD, your engine size etc. There is no limit to describing your problem. It enables us to get a very precise answer to your very precise problem quicker.

Look over the suspesion. You may have sway bar or leaf spring broken or loose.