You can buy a tray that fastens underneath the tank - very easy to install. Do a search for Toilet Drip Tray and you will see what I'm talking about.
The condensation is caused by the cold water which runs into the tank when it's flushed. Mostly a wintertime problem. The surface of the tank gets chilled. I think I have seen toilets with insulated tanks. If you're not up for replacing the toilet, the cheap fix is to wrap the tank with some sort of fabric for insulation. You can usually get these in a set with a matching cover for the lid. The other, slightly more involved, solution is to pipe hot water to the toilet with a mixing valve you can use to warm up the cold water a bit.
I have found that tanks continue to sweat when covered in fabric, and have not heard of using a mixing valve, and would be concerned that, if it failed, it could allow hot water to the toilet, which could crack the ceramic, or melt the wax seal under the bowl. At any rate, most sweating is due to high volumes of cold water going through the tank, which may be because the ballcock (fill valve) or flush valve do not seat off properly, allowing water to trickle through when toilet is not being used. Also, there may be a leak in the vicinity that evaporates and causes high humidity in the area, therefore more condensation. Running a bathroom exhaust fan more may help.
Your toilet may be running due to a faulty flapper or fill valve. To fix it, you can try adjusting the chain on the flapper or replacing the flapper or fill valve if necessary.
Your toilet may still be running due to a faulty flapper or fill valve. To fix it, you can try adjusting the chain on the flapper or replacing the flapper or fill valve if necessary.
Your toilet may be running randomly due to a faulty flapper or fill valve. To fix it, you can try adjusting the chain on the flapper or replacing the flapper and fill valve if needed.
Your toilet may be rocking from front to back due to loose bolts securing it to the floor. To fix this issue, you can try tightening the bolts at the base of the toilet using a wrench. If the problem persists, you may need to replace the wax ring or shim the toilet to stabilize it.
Your toilet may be leaking from underneath due to a damaged wax ring or a loose connection between the toilet and the floor. To fix it, you can try tightening the bolts that secure the toilet to the floor or replacing the wax ring. If the issue persists, it may be best to seek help from a professional plumber.
Your toilet water may keep running due to a faulty flapper or fill valve. To fix it, you can try adjusting the chain on the flapper or replacing the flapper or fill valve if necessary.
Your toilet may be running all night due to a faulty flapper or fill valve. To fix it, you can try adjusting the chain on the flapper or replacing the flapper or fill valve if necessary.
Your toilet rubber seal may be leaking due to wear and tear over time or improper installation. To fix it, you can try tightening the bolts connecting the toilet to the floor, replacing the rubber seal, or seeking professional help from a plumber.
Your toilet may be leaking from the bottom due to a damaged wax ring or a loose connection. To fix it, you can try tightening the bolts at the base of the toilet or replacing the wax ring. If the issue persists, it may be best to contact a plumber for further assistance.
Your toilet may be rocking due to loose bolts or a damaged wax ring. To fix it, you can try tightening the bolts at the base of the toilet or replacing the wax ring. If the issue persists, you may need to seek professional help to ensure proper installation and stability.
Toilet bolts can rust due to exposure to moisture in the bathroom. To fix this issue, you can replace the rusted bolts with stainless steel ones. To prevent rust in the future, you can apply a rust-resistant coating or use plastic toilet bolts instead.
Your toilet may be gurgling due to a clog in the drain pipe or a problem with the venting system. To fix it, you can try using a plunger to clear any blockages in the toilet or drain pipe. If that doesn't work, you may need to call a plumber to inspect and repair the venting system.