seedlings must be kept moist for the 1st week or so don't worry about overwatering until they have a little bigger rootsystem. it will only take a few hours for a seedling to dry out and dy if underwatered as they are so small they don't have enough leaves/stems/roots to retain much water.

as long as the light is the right spectrum
(cfl, flouro, mh, even hps) and the proper distance seedlings should not need to be supported. if you need to support them then they are stretched and you should have had the lights closer or have better grow lights.