What are the exact problems you're having? Support isn't there for script help, hand-holding, etc... So, if your tickets aren't directly related to a problem on their end, I wouldn't expect a quick reply.
If you're having trouble with a script or coding issue, you're probably better off asking here in the appropriate forum category.
You can also find an answer to many questions in the wiki.
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I've never run into that problem. You need to include every piece of important information in the first ticket. Be specific.
This is not how a support conversation should go:
Customer: My site doesn't work.
DH Support: Which site? What doesn't work?
Customer: example.com. I get errors.
DH Support: What errors? What are you doing when you get them?
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