Thoughts about tri bar / trekking bar on hybrid bicycle I have an hybrid bicycle Firefox Rapide 21S. I ride regularly around 40 KM. 

In headwind I feel like I should be in aero position so sometimes I put my elbows on my handlebar and it helps to reduce the drag. But that position is not very comfortable when my elbows are resting on flat handlebar. I have flat stem and already have lowered the stem. I also have bar ends.

I'm thinking about adding clip-on tri bars for more aero position, or I can relax my hands on for long rides.

I also thought of replacing riser bar with trekking bar, for more hand position, and also I can put my elbows on trekking bar which can be more comfortable because of bar tape on handlebar.

Is tri bar on hybrid a feasible option? Or trekking bar will be good choice? I would like your thoughts which could be better option.

Or should I simply replace my handlebar with bullhorn bar which would be great. But will my existing brake/shifter will work on bullhorn bar?
Aero bars (this is the actual name of what you call "tri bar") is surely a comfortable and affordable solution. In the Netherlands you see people with aero bars on hybrid bikes quite often - it is very common way to use the bike for a long commute and ease of manoeuvrability in the city traffic.

The only disadvantage of a simple version of aero bars is that you don't have the shifters and brakes there. For the shifters it's just inconvenience, for the brake handles it is also safety issue.

Bear in mind that aero bars have some pads designed for the elbows (or actually forearms) support and nothing (even thick wrapped bar) will beat it. 

Don't forget that the distance between the saddle and the bars should not be too long - when your body leans forward you shouldn't be stretching too much to reach for the handlebars. Otherwise you risk lower back pain on longer (in my experience >40km) journeys.

Concerning the bullhorn bars - in my opinion there won't be any added value for you except for the looks of the bike. And whether the brake handles and shifters are compatible depends only on the diameter of the bar you are replacing.