Related: how many protons per second can the LHC accelerate?
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This answer from another question says:
Each bunch of protons circulating in the LHC at full power will have about 120 billion protons of 14 TeV each, i.e. $1.6 \times 10^{24}$ eV which is about 250000 Joules.
Additionally, the comment below says that there can be up to 2808 bunches in the ring at a given time. Note also that the per proton energy should be 7 TeV/proton, not 14 TeV.
The circumference of the LHC is 27 km. Dividing by the speed of light, you find that the particles take 90 μs to complete a trip around the ring. Combining this with the numbers given in the linked answer, we can answer your questions:
What is the total kinetic energy per second of the particles accelerated by the LHC?
The total kinetic energy per second (i.e. power) passing through a given slice of the beamline at full capacity is:
2808 * 125000 Joules / 90 μs $\approx$ 4 Terawatts
Related: how many protons per second can the LHC accelerate?
The rate of protons passing a given point is:
2808 * 60 billion protons / 90 μs $\approx$ 10^18 protons/second
However, this isn't really "many protons per second can the LHC accelerate", since the LHC operates in cycles of filling up with protons, accelerating, and dumping/colliding.
