unless you are in a desert, you don't need a dome for a seedling. clones, maybe...
window may not provide enough light. it may stretch - grow tall and weak. keep eye on it.. provide greateer intensity of light if it starts to happen -- stem will grow paler as it stretches more.. get weaker.. avoid that if you can.
seed is packed with energe for a couple weeks. hopefully the compost isn't too hot.. probably fine.. but don't feed until a hint of fade -- likely on the 2 inititial cotyledon leaves -- then, it's ready.
just stay out of the way of the plant. it does all the work. if something goes wrong, assess your behaviour.. don't assume you ahve to do something.. it could be that you are doing too much :) i only say that to help get in right frame of mind, and it should help reduce OCD feelings :P
the plant does all the heavy lifting. provide light and water, and feed when it asks.