The light green floating mats are Filamentous Algae. Spraying them every 2 weeks with Cutrine Plus will work. The plant in your hand looks like bushy pondweed. Reward/Tribune, Aquathol K/Aquathol Super K, Hydrothol 191 (can be toxic to fish if used or applied improperly), or Fluridone (Sonar A.S.) all will work on that.

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3/4 to 1 1/4 ac pond LMB, SMB, PS, BG, RES, CC, YP, Bardello BG, (RBT & Blue Tilapia - seasonal).