As far as their ability to handle correspondence, it's a huge bureaucracy. Letters coming in to Writing Correspondence have to be scanned, converted to text, names indexed, then it might be handled. It can take many months if it's something they actually decide to research. Frankly, it can take months if they pull from the database of previously used answers, doctor it to include a quote from the original letter, and then go through dozens of proofreading and approvals. And a lot of the times they send a copy of the letter to the local congregation elders with instructions to handle the matter.
Service Department will be much more specific about handling letters from the BoE and CO/DOs. But they use lots of form letters, cut-and-paste, too. Usually if you try to call in, you get an idiot that basically tells you to write a letter.
None of this "questioning correspondence" stuff is what the GB wants. They want unquestioning obedience and adoration. Any questions should be handled by the underlings in the congregations. Problem is, the elders have no time or training to handle intelligent questions. They're unpaid, untrained, janitors. And any elders that actually care about people and want to do what's right are getting completely burned out. And the GB can't seem to figure out why.