I'm also 5'7 and 145 lbs, and can confirm this is not "overweight". It's a bit on the high side for distance runners (I ran my marathon PR at 133 lbs) but shouldn't be the sole cause of injuries.
My advice: take it one step at a time (litteraly). I am myself recovering from a calf strain and this is a lengthy process. Can you walk without pain? Walking a bunch is a good way to recover. With regards to your injuries:
Iliotibial Band Syndrome --- there is plenty of litterature out there linking it to weak hip extensors. Work to strengthen your hips and glutes (in particular, the gluteus medius). THIS IS VERY IMPORTANT FOR RUNNING IN GENERAL. Worth seeing a PT if it helps.
Plantar Fasciitis --- stretch your calves after running and have a massage therapist work on it too. I used to think stretching was for idiots, but in particular for the calves muscles, you want them to NOT constantly pull or be tight.
Calf strain (I have had sore or tight calves before, this was different. It just suddenly locked up on me out of nowhere mid run, I wasn't even going fast. 2 months going to a sports therapy to get it worked out.) --- I have that myself now. Same thing: strengthen muscles around, stretch calves, warm up before runs (I walk almost a mile), start runs slow, avoid speed work and hills for a bit.
Stress fracture in my foot --- never has a SFX, so do check your nutrition, calcium/bone density, make sure you don't have huge imbalances in your gait. Look, even pros get them. It must truly suck and I empathize.
Patellar tendinitis and Patellofemoral Pain Syndrome --- had them too at the beginning of my running career. Do you do much on treadmill? That's harder on the quads, same as downhill running. Honestly mine were cured by more running, but also taking it slow and building mileage slowly.
I personally became less injury prone when going from 3 or 5 days/week to running 7 days a week. I just do a bit less, I am careful, and try to build consistency. The rest (sleeping well, eating well) is just as key.
I am a 2:56 marathoner and last night ran 3 miles @ 10:00 min/mi because I'm still recovering from that calf strain. Again take it one step at a time. When I started being able to walk without limp again I was happy. Create mini goals. If you love running like I do, any running is good. Separate the wishes (e.g. 100 mpw and 2:30 marathon) from the simple things that make you happy (being 35 yo, active, and being able to run!). Don't let frustration take the fun out. If you need a few weeks or even months completely OFF and can live with it, then absolutely do. Just hoping you'll be back! Best of luck to you.
PS. My injuries have included PFPS, Achilles Tendonitis, Peroneal Tendonitis, Hamstring Bursitis, Calf Strain, Ankle Sprain, Lisfranc Joint Sprain, Shin Splits, Posterior Tibial Tendonitis, Calcific Bursitis on the Hip Joint, Popliteal Cyst Rupture, and I don't even know the others. I mean, I went from one to the other fixing things up one at a time. They come in less now than in the past, and I never hear back from most of them. Right now I just need to deal with that stupid calf! It's not even a bad strain (grade 1, no pop) yet I still have achy feelings for weeks.