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It is possible to relocate your camellia. The best time to sever a plant from the ground is in the fall. However, as long as deciduous plants haven't refoliated, you can still dig. Make sure you dig a rootball 10-12" wide for each inch diameter of the trunk. If your camellia trunk has a 2" diameter, dig 20-24" diameter rootball. Use the same transplanting method as you would any tree or shrub You will need to take care (water) for the camellia for the first year until it becomes established.

The standard rule of thumb is "no more than a third". However, IMO, if a shrub looks really leggy, it's safe to trim further. If your plant is heavily stemmed, you could take the entire mass back 1/3, then take the stems, one at a time, back another 1/3. As one stem starts looking fuller with new growth, cut another until the entire shrub is "short and phat". I've done other plants this was and have had success.

Grass clippings should be composted before being used as a mulch. They rob nitrogen from the soil, the element camellia's love. Also, place the mulch no closer than 4'' to the trunk, this allows for air flow. Mulch should only be 4'' deep unless it's non-packing leaves like pine needles or oak leaves. You don't want the plant to smother.
Your hedge may be trimmed to encourage shrubby growth. I would not place a lot of stress on it by overfertilization. A light dose is advantageous, but let the plant "get it's wits gathered back up", before trying to push a lot of new growth. Once the hedge is growing, you can take up to 1/3 of the plant.