What do I need to do to be able to make sure that any new installed programs that I install do not "phone home" and are not spyware in disguise and do not send personal data from my hard drive back to their server? Is that possible to stop or make sure it don't happen? What exactly do I need to do to make sure nothing sends personal and private data out of my laptop?
Only install reputable software you can trust and feel confortable with. If you start entering into the "call home" paranoia then move to Linux for which you can inspect source code (assuming you know how to read it). Most windows software (including the same OS) calls home nowadays and its normal they do so. There is nothing to worry about unless you need to hide something. Threads comes from outside malware not from "call home" activities originating from legit applications.
My main concern was a program called Time Freeze by Toolwiz. Sounds good program, but there is not much feedback about it and some people on the internet say they are concerned about the program and what it might be doing. How can I install it and be confident it's not sending any personal data anywhere?
You can't 100% unless you access the source code, as per above you simply pass on and choose some other restore software. There are several users here using other solutions, just search the board or the thread about security setups