Short answer:
No, there are currently no rules about what happens if you sleep in armour.
The are rules about how fast you can don and doff armour [pg. 146 PHB] that's quite kind and fast (you do not don full plate in only ten minutes in real life) so characters shouldn't really have any issues with switching in and out of armour.
The are however rules for swimming in armour. Page 183 in PHB under the heading Suffocating. It's what you use to simulate drowning which is what happens if you try to swim in armour, especially the sort made primarily of metal.
Long answer:
Sleeping in armour while not ideal or the perfect recipe for a great night's rest isn't as bad as you'd think. Anyone who ever played hockey or American football knows that laying down and rest in all that padding and equipment isn't bad.
People all through history have actually slept and spend long times, sometimes months at the time, pretty much constantly wearing armour both day and night. The great siege at of Malta is one such example. Another example though a non-combat one, is how the moon astronauts slept in their space suits during breaks between the moon walks. Even now modern soldiers are sleeping while wearing body armour.
Now some might point out that modern battlefield body armour is designed to be comfortable. But that's just it. All armour through the ages has been designed to be comfortable to wear, to move in and to rest in because otherwise no one would be able to use it during long periods of combat. Full plate is both agile, flexible and feels light to wear.
Second thing to think about is that humans are adaptable and can learn to endure the harshest conditions (can't speak for those poncey elves though). The human brain can actually tune out things it finds annoying or distracting over time. So even if it is uncomfortably to wear armour you forget it after awhile.
Which bring me to my point. (Finally right.)
If the reason you want rules for sleeping in armour is realism you don't really need rules as the effect of a night in armour would be negligible for a fit person trained in wearing armour.
You might give the players a disadvantage for the first roll they make after waking up if they make sleeping in armour a habit.
But the truth is that the cold, wet and fear of sleeping outside in a dangerous situation have much greater impact on how well rested you are than if you sleep in your armour or not.
However, while sleeping in your armour might not be that bad for your rest, prolonged armour use without breaks will eventually lead to all manners of unpleasant side effects. For example there is something called pressure ulcers also known as bedsores. They are incredible painful and nasty. Another nasty effect is spinal compression.
Now there might not be any rules for those effects either though if they were they would most like be in the form of sickness and injury than anything else. Still, Google some images of bed sores and show your players and they might start removing their armour a bit more often.
Both require you to be submersed in water to work. Now, if you were to fill the Bag of Holding with water first ... I'd say the Manta Ray cloak still doesn't work infinitely, because there's only so much oxygen in the water you can breathe.
The Cap however creates a bubble of air around your head, and doesn't insinuate in any way that the oxygen is taken from the surrounding water.
Best Answer
You can do whatever you like; what I would do is play it as written.
PHB p. 144
As it says, if they are strong enough they suffer no penalty to speed, if not then they lose 10 feet of speed.
PHB p. 182
As it says, a creature without a swim speed uses 2 feet of movement for every 1 foot covered (3 if difficult terrain). A creature with a swim speed moves 1 for 1 (2 for difficult terrain). As phrased, a swim speed does not exempt you from making a Strength (Athletics) check if required.
Significantly, it says nothing about the effects of armor on swimming.
Does this make a lot of sense? From a game perspective, yes - it gives simple rules that can be used with a minimum of complexity.
Can you rule that armor should make a difference? Of course, it says you can right on p. 6 of the PHB - if the PC says "I swim across in my Plate armor" then a perfectly sensible ruling is "You sink like a stone", however, given that this is not what the rules say, fairness dictates that you tell the player the consequence of their action before they undertake it and also before they make a commitment to spend in game money on an expensive anchor.
DMG p. 159
As it says, it gives you a swim speed - take that and apply it to the rules above.
TL;DR
Question 1
"can they swim 60 ft as the DMG says (pg 159)"?
Yes
Question 2
"are any of you DMs ruling that there are some penalties to swimming in heavy armor even with a swim speed?"
I cannot speak for "any DM", but by the rules in the book: There are no penalties to swimming in armor with or without a swim speed.
Question 3
"Would you include a higher Str requirement with swimming?"
Me? No, by the rules in the book: The cloak gives you a swim speed of 60 feet. If you meet the strength requirement, there is no penalty to your speed; if you do not then your speed is reduced by 10 feet (i.e. to 50 feet).