Is loss of appetite, weight loss and weekness common in sciatica?

Not really. Weakness could be, but the appetite loss or weight loss is not a typical problem with sciatica. See your PCP to figure out what is going on.
No. Sometimes the lack of treatment for pain brings on feelings of depression which causes your symptoms. Otherwise, symptoms you describe are seen in serious medical conditions and may be unrelated to your sciatica (a common complaint that should be responding well to treatment such as walking, exercising and avoiding heavy lifting).
Sciatica. Absolutely not, weakness maybe but only in affected leg. Sounds like u may have more systemic problems. Go get checked.