Yes they can. Antidepressants known to cause weight gain, like tricyclics and mirtazepine, can increase lipids. Those that are more weight-neutral (like wellbutrin, effexor, (venlafaxine) and cymbalta) are less likely to do this. Http://www. Ncbi. Nlm. Nih. Gov/pubmed/16774491 there could be other factors in this besides weight gain, but they're so far unknown.
Some. Yes. Some of them can cause hyperlipidemia.
No, but. Antidepressant are not related to changes in the lipid panel. However, many of the antipsychotic medications to increase lipids, especially the triglycerides. Without knowing which one your are specifically asking about, it's hard to say.