The second one certainly is not critical, not sure about the first one. You should be able to find someone qualified in your area to do some welding for you. 

The strap under the seat is of low consequence. It can be re-welded in place once all the plastic is removed from the area. Probably the weight of the rider coupled with bad rear shocks did this, and those are not normal conditions.

The strap at the head post is what bothers me. This plate stiffens the steering head post, which is what gives you precise steering. The forces that generated that crack are from head-on. Each time the front brakes are applied or the bike rolls into a stationary object, this crack gets a little worse. And the worse part is that it's in a bad place to weld. You'd need to slip a specially cut piece of metal in there behind it to back it up. Welding this backup plate would mean stripping the frame and turning it over. Even then the placement is nearly impossible. The labor involved is just not worth it. Get another good, used frame. 

All those shops on eBay selling engines and forks are left with a BIG pile of frames. Just remember to get the paperwork.

Posted by: @wobbly

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The strap under the seat is of low consequence. It can be re-welded in place once all the plastic is removed from the area. Probably the weight of the rider coupled with bad rear shocks did this, and those are not normal conditions.

The strap at the head post is what bothers me. This plate stiffens the steering head post, which is what gives you precise steering. The forces that generated that crack are from head-on. Each time the front brakes are applied or the bike rolls into a stationary object, this crack gets a little worse. And the worse part is that it's in a bad place to weld. You'd need to slip a specially cut piece of metal in there behind it to back it up. Welding this backup plate would mean stripping the frame and turning it over. Even then the placement is nearly impossible. The labor involved is just not worth it. Get another good, used frame. 

All those shops on eBay selling engines and forks are left with a BIG pile of frames. Just remember to get the paperwork.

Thanks for the advice! I wonder how registration works if the frame is swapped? Does anyone here have experience with that? Specifically, I live in NY and would get it registered here 

@allen-schroeder 

Gemini provided a pretty good answer, but consult your local DMV...

https://share.google/aimode/zmOQWHRlXluJAEKHN

In New York, the motorcycle frame is legally considered the core identity of the vehicle because it bears the Vehicle Identification Number (VIN). Swapping a frame requires updating your title and registration through the New York Department of Motor Vehicles (DMV), often processed via a custom/reconstructed vehicle inspection path if the replacement frame has a different VIN or lacks an active title. [1, 2, 3]

It's worth reading more at the google link above, as it has details about documentation required...

I wouldn't give up on that frame just yet. 

The weld on the rear sub frame isn't much of an issue until it cracks all the way thru. A mysterious wobble may occur at various speeds. As Richard says, it's an easy repair to simply grind off the paint and weld over it. If you were to survey a group of bikes at a tech day or camp out, you would find many of those welds cracked or repaired.

The steering head gusset is another story. If that gusset is cracked all the way thru, the other welded structures on the steering head portion of the frame are what is holding it together. It would be best to engage an experienced welder to make that repair. Welding on the vertical plane is tricky. 

I have a slightly different view...

The crack at the head post MAY be the result of a serious crash, in which case the frame may hold other hidden flaws, such as mis-alignment. When this goes undetected, the front tire starts to wear on one side. The rider doesn't realize it, but he's having to steer to make the bike roll straight. 

In my years as a mechanic I repaired many wrecks. Even when the crash is "head on", the forks usually get pushed left or right. It is hardly ever perfectly "straight on". We had a long 1" steel rod that had been turned to a point. We mounted that rod in the head post on cones which centered on the fork bearings so that the tip told the true center of steering. Then we would take precise measurements from that tip to motor mounts on the left and right side. Also bubble level readings... vertical on the rod while indicating horizontal surfaces on the frame. Here's a photo of this system in action...

Obviously, that's not a BMW, but the same rules apply. There are immense impact forces in a wreck. The rider gets thrown off and eventually gets straightened out, but the steel always remembers by staying in the new position. 

It would be well worth your time to look closely at the L & R fork stops on both the frame and the triple tree. The triple tree may be new, or the frame stops may show evidence of being welded up. 

One thing for sure... that's not a fatigue crack from simple vibration.