Guy Martin is obviously a decent cyclist, but you should note that his record-breaking ride occurred under very special conditions. For starters, he built his own frame (or rather Jason Rourke built it for him). Next, he chose exactly where the run would take place - on sand flats. And not least he was towed in order to get up towards top speed, which dramatically reduced air resistance.
All of these things make comparing his ride to how you would ride, like comparing apples and oranges.
To get an idea of speed, you'd probably get more from looking at professional road racers. These guys will typically ride at speeds of maybe 40+ km/h. Put them on specialist time trial bikes and they will top 50km/h. And these are average speeds - you can imagine that gradient, wind and the ability to slipstream will be factors plus or minus. Certainly when descending, the 70km/h you mention is not all that much for them - I myself have gone at more than this speed and lived to tell the tale (I am far from being a fast rider).
But you need to bear a couple of things in mind. First, these people are professional athletes, which immediately sets them apart from the rest of us, their bodies are something south of 5% fat, and you can see that the muscles they have developed for cycling are disproportionately large. Second, the bikes the pros ride, a ballpark estimate of cost would be maybe $15000 - which buys you a lot of lightness. The typical weight of one of these bikes I'd guess is no more than 6 or 7 kilos.
Transpose all of this to you. As regards the roads you ride, how good will they be? Basically, the smoother the road, the faster you'll travel. If you had a road bike, how light would it be? Plus there's you - how fast would your legs take you? These are all factors that would affect how fast you could ride.
In answer to your specific points, as I said 60-70km/h is not a great deal under certain circumstances. I would imagine most road bikes could achieve this. So as to where you'd get them, the answer is pretty much anywhere. How often you could reach these speeds would be down to you.
Your second point, re stability. I'd argue that stability is as much a factor of the bike as the speed. One of the big differences you would notice between, say, a $1000 road bike and a $15000 bike would be stability. A lower end bike should be pretty stable, but will have limitations on performance. A higher-end bike will perform better but will also require more skill to handle. I have observed this to be true regardless of speed - high-end bikes are more responsive and therefore more "twitchy" (I'm thinking of stability here as how easy it is to control the bike). Its a bit like going for a ride on a donkey and going for a ride on a thoroughbred.