No.
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HM 8 doesn't exist in Pokemon Fire Red or Leaf Green.
Waterfall is HM07 in Pokemon Gold, Silver and Crystal only. There are 2 Pokemon in Red and Blue who can learn it naturally (Goldeen and Seaking) however because its an 'old' attack, you may trade over some red or blue Pokemon, teach it to them in Gold or silver and trade them back. This is the only NEW HM that can be taught to old Red and Blue Pokemon, HM06 Whirlpool doesn't exist in red and blue.Waterfull is not an HM in Pokemon Red or Blue. The only Pokemon that know Waterfall in those games are Goldeen and Seaking, which Goldeen can learn Waterfall at level 37, while Seaking is at level 39 in Generation I.
after you meet the captian and he gives you the CUT hm, the boat leaves after you get off and it dosent come back.
you can't get back there unless you get the HM SURF OR HM FLY.Once you get that hm you can fly to the city or use surf from fuchsia city from where you have to cross the seaform islands and cinnabar island . its better by using fly
HM08 doesn't exist in firered.