I did a 20 km ride (total roundtrip) when I was in junior high school. As a kid, I even sucked in running but physically healthy. I don't mean to brag, but if you don't have any serious illness I think 15km is ok.

How about having long stem spacers? you can play with it to get more comfortable.

I second this, use your current bike as a bike donor and buy a new frame probably will cost more since you need to buy bike tools (socket drive, allen keys, chain breaker, bb puller, crank puller, etc). All these tools probably will cost $100 - $150.

1" is okay, for me, I fell of my bike twice because of black ice and top tube isn't really an issue, moreover, If you fall, the bike will be leaning right or left, so probably you still can stand on your own feet.

The biggest issue is tire clearance especially on the chainstays, make sure your frame can accommodate >32mm tires.

I second an SS bike, buy a cheap bike frame with used components

Looks like it uses v brakes which means you'll get a problem when attaching brakes if you use 700c tires