All of the situations you outline are emergencies.
the appropriate way to use the VHF is to dial up channel 16 (unless there's a USCG emergency channel or other special rules published for your location).
Break in with "mayday" (m'aidez for all you frenchies) repeated three times, state who you are, where you are, and what you need. repeat. with a named vessel you would use the vessel name, I guess on a kayak you could say "kayed [your name]" or something. actually the emergency call is officially "pan pan pan" but that's like asking an american about centimeters (centimetres for all you frenchies).
e.g.
"mayday, mayday, mayday. this is the sailing vessel Gi-Gi, Gi-Gi calling on channel 16. We are 22 miles south southeast of key biscayne. we have a diver who is unconcious and unresponsive. we require immediate assisstance. repeat, we are 22 miles south southeast of key biscayne. we have a diver who is unconcious and unresponsive and require medical assisstance. over"
USCG should come up and have you switch to another channel
"sailing vessel gi-gi this is the us coast guard. please switch to channel 42, channel 42 over"
you reply with the channel, wait a second to make sure they don't correct you, then switch. when you come up on the new channel hail the coast guard. don't switch without reading back the frequecy/channel they give you and give them a second in case you heard wrong.
"roger, s/v GiGi switching to channel 42 over".
[pause switch to 42]
"coast guard, s/v gigi on 42 over"
then follow their instructions
note: many boaters do not overserve proper radio ettiquete. frequently you will find people chatting on channel 16. (<soapbox> usually power boaters, not sailors. usually the cheaper/smaller boats where only skill required to operate the boat is being able to write a check </soapbox) Don't be afraid to break in and tell them to shut up or move it. 16 is NOT ship to ship/shore party line
if you are using a hand held, particilarly if its a low wattage and/or you are using a rubber ducky antenna and the antenna is low to the water (kayak) you might not be able to hail the USCG or whomever. If you get no answer with a couple of calls you will need to ask for a relay.
"mayday, maday, mayday. this is the s/v GiGi. we are 22 miles south southeast of key biscayne with a medical emergency. does anyone copy? over"
<another vessel responds> "gigi this is the container vessel ichin maru (yeah right) near your position how can we help? over"
you can either direct them to another channel and then ask them to call up USGC for you (personally I wouldn't have them leave the channel in a real emerg.) or just ask them for a relay on 16.
"ichin maru this is gigi. we have a medical emergency and can't raise coast guard. can you raise them and give us a relay? over"
the other vessel will make the call for you and relay your conversation. you will probably be able to hear CG but not the other way around.
how many parachute flares and orange smoke flares do you carry? ha ha