You do know that the space shuttles have been decommissioned right? Also, sense the International Space Station has no heat shield it would just harmlessly disintegrate in the atmosphere just like the space shuttle's external tanks and all meteors of that size.
NASA space shuttles have been, yes: this wasn't NASA's doing, NASA didn't exist at the time.
A v-pulse was used, as well: it's hard to explain just what they do. Think of it as an explosive whose entire force goes into the shock wave, with very little wasted on heat or light. The sheer concussive force creates a localized vacuum, with all the molecules pushed to the side. The ISS was in pieces, but the terrorists made sure most of those pieces had little contact with any atmosphere.
In your time, do they ever find out what UFOs are? Aliens? Government crafts?
Not to my knowledge. They may be a myth: or they may be other time travellers. There are a lot of unexplained events like that; a lot seem to me to be perpetrated by people from the future. While I was planning my journey back, I was going to have support a few years in the future: then if I needed to send a message, I'd carve a crop circle in a specific pattern: that glyph would be interpreted. The advantage of that, was that there's no way it could be stolen, and anyone with the knowledge could read it.
I didn't, in the end: it was too unwieldy, and sadly she didn't survive long enough. However, that doesn't mean other travellers couldn't have used the same system.
So that leads me to my question... how does your time machine work, Mr. Titor? Do you think we could replicate the technology that you use with today's tech? Most hypothetical forms of time travel rely on controlled singularities, similar to the weaponized singularities that you describe as being utilized by CERN. It is theorized that if you take two singularities, contain them in some form of magnetic casing, and reverse the poles, you can bend spacetime for a sort of time displacement effect. Is this what your time machine achieves? Or does it use a different form of technology?
I believe that technology is the kind used by CERN. There are advantages and disadvantages: the obvious disadvantage to that mechanism is that it requires a lot of power and machinery to operate, and would usually be one-way. That's one of the reasons they don't travel back to before they took over: they'd be stranded, and if they prevent their time machine being built (the hummingbird effect's a killer) there's no do-over.
My time machine was designed by my father. He used to work for CERN, but he left to aid us in the resistance. The basic idea of mine is to remove the middleman: black holes aren't used to manipulate spacetime, we tweak it directly. If you've heard of string theory, I think the idea in this time is that all matter is made up of certain vibrating strings. This is an extreme simplification, but the idea is to cause those strings to vibrate: those strings exist in more than three dimensions, so if you set up a resonance, you can 'push' matter along those strings. If the device which causes the resonance is pushed as well, then two-way travel is feasible: you wouldn't end up at a time without the machine.
As for whether it could be recreated, I do not know. My father was the designer, not I: my understanding is rudimentary. I designed the stabilizers (to tether it to a geographical location: it's not good if you tarvel back in time but stay fixed in space, the movement of the Earth would see you lost), and a few finishing touches, but the heart of the time machine itself isn't my design. I wouldn't know how to build it, without tearing it apart and peering at it piece by piece, and I'd rather not do that.