Newbie Question - New Tank

I set up my 1st tank 10 days ago. I bought 3 plants from Petco - nobody
there could identify them, but they seem to be doing well. One plant
looks just like "miniature wheat" about 4 inches tall. I THINK this
plant is "spewing" stringy material around the tank in order to
reproduce. "Threads" are appearing everywhere and small plants are
springing up, but they don't yet look like the plant I suspect of

Are these "strings" identifiable as a plant reproducing, or do I have
some type of algae cropping up? Is it perhaps a fish disease? I have had
a number of fish die - I assume it was stress, but I'm new and learning
the hard way. I want to make sure this is a plant life-cycle "thing" and
that I don't need to rush out and find something to treat a rare
fish-disease that only newbies experience......

Any email replies will be most appreciated! As will discussion on this