Can chronic sinusitis cause feeling of something stuck in throat and bad breathe? and can it be viral?

Yes: Yes, chronic sinusitis can cause bad breath and mucus - feeling like it is stuck or dripping into the back of your throat. If your symptoms are chronic, that is, having lasted for more than 3-4 weeks, it is less likely to be viral and more likely to be there because of a bacterial or fungal infection. Also underlying allergies are often a contributing factor to the development of sinusitis.

Sinusitis: Chronic sinusitis can cause the symptoms you mentioned but once it is chronic it is no longer viral. For best management of your symptoms, consult an ENT or allergist.