Does the caller (Da'ee) bear sin or punishment if he invites someone to a forum for the purpose of benefit, but the invitee's responses are not in accordance with Sharia (such as being jocular or irreligious), while the caller knows that the invitee will not respond to advice?

The question is unclear, but if the intention behind inviting him to participate was for mutual benefit, and you did not anticipate his transgression, then you bear no sin for what he does; as Allah Almighty says: "And no bearer of burdens will bear the burden of another." You should continue to advise him gently. Laughter is permissible as long as it does not exceed the limit, in which case it becomes disliked. The ruling on placing faces varies: it is forbidden if they are hand-drawn or pictures that contain fitna (temptation/strife). As for photographic images of non-women that are free of fitna, there is a difference of opinion regarding them.