Can you mow (Leucojum aestivum) summer snowflake once they have stopped blooming?
The foliage lasts a long time on Summer Snowflake, this foliage should stay on the bulbs to feed them for the next seasons flowers.
Wait to trim the leaves until they have begun to die back naturally.
https://www.gardeningknowhow.com/ornamental/bulbs/snowflakes/growing-snowflake-bulbs.htm
Do I have to wait until plant goes entirely brown or can I cut them back while still green but falling over? I love the plant but would like to put something else there for the summer.
If you are referring to leucojum plants, these grow from bulbs. The bulbs need nourishment from this year's foliage to ready them for next spring's show. For best bulb health and future flowers leave the foliage in place until it yellows. When that happens, feel free to cut of pull it off.
The leaves are yellowing. I have three in pots that have part shade and sun. What do they need?
Yellowing is most often associated with a lack of nitrogen. These should be fertilized at least once per year. Dolomitic lime helps to buffer the soil pH to a more appropriate level if it is out of balance. Both of these together will help them to come back to their original color.