Welcome. We were all new to this once upon a time! Browse around lots of older posts here (and use the search function a lot) and you'll find plenty of great information.
The IEEE-1394 ("Firewire") standard itself only specifies the physical (size & shape of plugs) and electrical (# and purpose of conductors, voltages, etc.) characteristics of the interconnection.
What it doesn't address is the data which flows over the wire. That falls into 2 broad categories - the control data (commands such as "play" or "stop" and status such as "rewinding", etc.) and the actual audio & video data.
Relevant control standards appear to include only 2 - the older AV/C (I believe this stands for "Audio Video Control") standard and the newer HAVi ("Home Audio Video Interoperability"). I'm not sure whether either standard refers to the A/V data format at all.
Audio/Video standards here are mainly the MPEG (Motion Picture Experts Group) family of standards. Since MPEG-2 is what is delivered directly by OTA (Over The Air) broadcasters (and Dish Network), this is the relevant standard for DVHS.
Whether a particular set of machines works together depends on which standards they support for the control & A/V data. In the case of the Panasonic PV-HD1000, the A/V data is an MPEG-2 bitstream while it appears they use AV/C control. We don't know for sure, but hopefully the new Mitsubishi will work with it. (I hope so too! http://www.avsforum.com/ubb/wink.gif
As for HD timeshifting, as you'll undoubtedly read in many posts here on the forum, don't expect to do any with your DVHS deck and DirecTV. Your only option there is analog (WVHS). If you're willing to switch to Dish, and invest some time & money (~ $1,300 - $1,500) in finding a Dish 5000 & modulator, you'll be able to build your own library of movies & specials from HBO, Showtime & Pay Per View.
Good luck, and enjoy your new hobby!