Gas bike frame with tank stability issues

[This_Toad]

Ok, so I just got my bike project to a ridable state and I've began dialing in the chain tensioner and such. Right away I noticed two things, one this bike has a huge potential for speed wobbles (although I haven't gone fast enough for that to really happen maybe 20 or 25 mph.) And two a very strange sensation while turning. I'm wondering how others have dealt with this type of thing. Do these frames have a tendency to bend while riding? Or is my geometry setup just not up to snuff? Any suggestions? Thanks!

specs:
79cc 4stroke predator clone
Gas bike frame with tank
Mag wheels
60cc flexible exhaust
30 series cvt/torque converter
(Modified for a jackshaft)
I believe 120mm travel front fork
(Could be less like 100, it's from a few years ago)
Long stem from a road bike
Cruiser bars

 

[darwin]

Do both tires match a centerline from front to back?

 

[Risk Man]

I have always thought that my aluminum gas tank bike frame (BSberry) felt like it "wobbles" from front to back suggesting it is "flexible" so to speak. While I have run up to 40 MPH and it seems stable enough, compared to my huffy build it does not have as solid a feel as a conventional steel frame bike. There was another member here that built the same bike as mine and initially he thought he needed to reinforce the front fork for seemingly the same reason, but ultimately said the bike was very solid and he was just fine with it.