Is 214/82 pb --> 0/-1e + 214/81 ti balanced

No, your equation is not balanced.

The main point to remember in balancing nuclear equations is that the sums of the superscripts and the subscripts must be the same on each side of the equation.  

Sum of superscripts: 214 = 0 + 214.  

Sum of subscripts: 82 ≠ -1 + 81.

Your subscripts are not balanced.

If the equation represents the β decay of lead-214, you must write it as

Correct Option B:  3 protons, 3 neutrons and 5 electrons

Reason: 
Since, particle 'Y' deflected at an angle (–5°) opposite to that of proton (+15°), this suggest that particle 'Y' has charge opposite to the of proton. In option B, there are 3 protons and 5 electrons. Thus, net charge is -2. 

Also, magnitude of deflection of 'Y' particles is less as compared to protons, this signifies that, it is very heavy as compared to protons. Both of this criteria is satisfied by option B. Hence, it is correct choice.