yes, it has four rings, but that doesn't mean that it belongs to the same family as the so-called tetracyclical antidepressants. the latter are structurally derived from the tricyclical ADs by closing a fourth ring, while the structure of trazodone is quite unique among ADs; it forms its own small category with some close relatives called serotonin antagonists and reuptake inhibitors (SARIs).
This is correct. It is not a TCA or tetracyclic, however it is an antagonist at the H1 receptor, meaning it is an anti-histamine at least to a certain extent. The only other drug in this category I know of is Nefazodone. Interestingly, both of these drugs are partially metabolized into mCPP which acts as a full agonist at most of the 5-HT receptors. Its guessed that its action offsets some of the 5HT2C antagonism which is why there is no weight gain with these two drugs typically. As an aside, I was one Nefazodone for a bit until I foolishly went off it suddenly and suffered horrible withdrawals (it has a relatively short half-life). Before that I would take it and be feeling like I was on a low dose of MDMA all day long with none of sedation that I was told might occur. In fact both Trazodone and Nefazodone didn't sedate me worth a damn. Now I take it and feel suicidal, which is unfortunate because it really seemed to be working well.