1. Showing pictures of LDD creations is totally fine--many people have done so in the past. To elaborate, here's a selection from the SBC Rules (and BBC Rules has a similar section) about what you need to post a topic:
All MOCs need pictures, or at least an adequate description. If you're posting a topic for your MOC, please have the pictures ready to go, or at least have a link to a pending-publication Brickshelf gallery (it takes 24 hours, give or take). If you know you're not going to have pictures, though, you're welcome to post a detailed description of your MOC, or instructions for making it. It's not unheard of for people to make MOCs and take pictures for other people, but you really shouldn't count on this. Please also remember that the best description cannot stack up to photographs, so do your best to get those pictures.
2. You're allowed to use custom parts in your creations, yes. If it's part of a larger MOC, then it'd be best to just keep it in the MOC topic, but if you have a specific custom piece that you want to portray, you may post a topic in General Art. Here's a quote from the General Art Rules, where Ziko answers this question:
Would things like custom masks, Bionicle and LEGO figures count? I suppose it could go under sculptures, but I'm not entirely sure.
Yes, customized creations like that go here instead of a Lego-Based Creations forum, since the customizing/art techniques are the focus rather than the Lego construction.
3. Punishment largely depends on the situation at hand. If I'm understanding your questions correctly, it sounds like none of these things would be against the rules (though if you have a lot of custom parts you want to show off, for example, it might be better to post them all in one topic rather than separate ones). Spam is a post that does not contribute at all to the topic or forum at hand. So posting your creations in other people's topics, for example, might be considered spam, but posting your own topics for your own creations would not be.
Does that clarify things for you? Anything else I can answer? =]