If there had been alien satellites in the solar system at that time, would radio astronomers have been able to intercept their communications?
Only if the observers were lucky and the satellites had no desire to hide their transmissions.
First, you have to be looking in the right direction, at the right time, at the right frequency.
But then you have to recognize that the incoming energy is a signal - which means that it has to be coded in a way that you can detect, and expect. 1950's technology still used fairly simply effectively analog modulations - signals of interest had lots of energy concentrated in narrow bandwidths. But many modern schemes are instead spread-spectrum and can only be detected by a receiver seeking a comparable pattern. Even something not trying to hide - say our own contemporary GPS satellites which transmit different coding sequences all in the same frequencies - would be difficult to detect as intentional radiators with 1950's gear, unless someone knew exactly what to build gear to look for. Something so close might be seen by reflecting sunlight or on an early active radar search, but that's distinct from intercepting its signal.
Would it have been possible for mid-20th-century terrestrial radio technology to send signals back to space, and establish two-way communication with these devices?
If the satellites were design to make that possible, then yes, most definitely.
If you wanted to communicate with an early electronic society, you'd go to efforts to make things easy. You might try some very longwave frequencies for ultra-primitive situations, and your classic physics-inspired SETI ones, but if you're orbiting someone's planet you'd mostly you'd pick the low VHF range where you easily get energy through an ionosphere, while remaining in the realm of what can be done with vacum tubes.
Then you'd use (at least at the outer attention level) simple modulations, for example toggling between two discrete nearby frequencies in such a way that you elicit a response from all of your basic detector types (BFO, AM, FM). And you'd use it in a way that creates a "curious" pattern such that a lifeform manually noticing the signal finds it interesting enough to bring it to the attention of someone who can hook up more instrumentation to look at it. 199
Finally, you encode your meaning in terms of basic mathematics - prime numbers and all that, and in a self-teaching way. Our own science fiction authors and actual real world outgoing contact attempts have examined the possibilities there.
To some extent though, to have a meaningful "conversation" you have to pack a fair amount of AI into that satellite. And if you're going to do that for the meaning, you might as well do it for the communication, too. In other words, you monitor your target civilization's own communications, and you respond in kind. If they call each other with a particular pattern, you use the same pattern. If their broadcast stations turn off a certain period after the local star rotates past the horizon, you jump in an instant later with your own "greetings planetenials" message - or simply replay their own traffic of the previous platentary revolution. In short, you get their curious individuals curious, and you make the task of responding within reach 209