You have a pretty thorough understanding of the process. To answer your questions:
• What kind of equipment do you use to record in the field?
There are no hard and fast rules but you should try to use as professional a product as you can get your hands on. A powered speaker is a must, so be sure you have a source of power wherever you are planning on recording. Re. microphones, many folks use DPAs or Earthworks, but Schoeps, ATs and Neumanns are all great choices. If you don't have access to any of those, use what you do have! You also have a choice as to how many channels you are going to record, ie. mono, stereo, quad or higher. What configuration you choose will depend on your recorder, how much time you allot for setup, and of course your application. If you are preparing for strictly ADR purposes then stereo would more than suffice.
• What deconvolver program do you use?
Altiverb is the most popular in film post-production (at least here in LA). Another choice is TL Space. Still another is IR-L from Waves (although I've not used it). Here's an excellent article from Sound on Sound regarding the various apps and how they compare.
• What kinds of applications do you [use] the profile for?
Totally depends on what you want to use if for! You could stay strictly within the constraints of treating ADR to match dialog (or whatever space you are trying to match into), or use it on music or sound effects to simulate a desired real-space. I often use Altiverb to change the original file altogether, to design it into something new. Also, remember that convolution reverbs do not have to use only impulse responses from real spaces; they can use any sound sample that you throw into it to convolve against something else, ie. an anvil hit used as an impulse response will impart a metallic characteristic into whatever sound you process.
Experiment and have fun!
PS. There are many 3rd party impulse response libraries out there for users of convolution reverbs. Here's one that I've enjoyed using from time to time.