When the WC blocks, how easy is it to get it clear? This may suggest how close the blockage is to the pan.
Vent is unlikely to make any difference, it's blocking because solids are building up somewhere in the pipework. By all means, install a Vent, (it can do no harm), Ideally Junction )Tee) would be stack end, but its not vital. What I would be doing is checking and adjusting the fall on the 'horizontal' section, as I suspect his may be where your problem lies. I'd be looking of a minimum of 50mm, ideally around 70mm of fall between the back of the Pan and the stack.
It is rare for Stacks to blocks in the vertical section, unless there is an obstruction holding solids back,, so I'd also look at any wastes connected to the stack, and ensure the pipework hasn't been pushed too far in, providing a convenient 'perch' for material to collect on. Lower down, the momentum of the falling waste and water is usually enough to push everything through into the drain, but it is also not unknown for there to be issues with a damaged rest bend at the foot of the stack, causing solids to catch and build up.