You don't need to drop the mast to replace a wire to the steaming light. Just attach the new wire to the old securely, and use the old wire to pull the new one up (you'll need one person aloft and one on deck).
To run new wires to the masthead for VHF and anchor light, you have to be more careful because you don't have another wire to help lead the new wires, so you probably shouldn't just drop a weighted string down the mast. The danger is that those wires will end up being in a place where a halyard will chafe through the wires insulation and lead to problems, so you might need to do those when the mast is down. You'll need a crane to do that. While you're at it, a great improvement is to use pop-rivets to attach a thin-wall PVC conduit to the inside of the mast, and then run all your wires through that. It'll make it easy for you to run wires in the future, and it'll protect the wires, as well as prevent them from tapping on the inside of the mast and keeping you awake at night.
Regarding your slack lower leeward shrouds, you don't necessarily want to tighten them just because they're slack. The leeward lowers will always be a bit slack because the windward shrouds stretch a bit. To see if the lowers are tuned correctly, you need to sight up the mainsail track while sailing on the wind. Search for a description of this process, or you can find it in any good sailboat maintenance book.
