Why is it "these" instead of "those" here?
Because there is TYTO (for male gender it would be TITO) as opposed to TAMTY or TY (TAMTI or TI)
Why not "persons"?
Já bych "persons" nechal pro "osoby", ale třeba to tam jen někdo opomněl a doplní to.
Why "These beds are good for elder persons" is incorrect?
"Elder" as an adjective is not used in this way. We can say, "He is my elder brother," -- though most would probably use "older" instead -- but we cannot say, "He is an elder person."
Although there is the adjective "elderly": "He is an elderly person", but I believe this is used as a sort of euphemism, or at least it is not as common. Any native speakers can confirm this?
I (native AmE) would say "elderly" is perhaps more formal/polite. It is often used to refer, for example, to a group as "the elderly" rather than "the old people." But, yes, you can refer to someone as "an elderly person."