After the end of Edge of Tomorrow, would Cage be caught in a time-loop?

Short answer: we don't know.

First of all, the answers to the question that you mention are inconclusive. So, did the blood give Cage the ability, or did it just include him in the one last reset dome by dying Omega (maybe like a post-mortem tick)? Personally, I believe that this was not thought through by the film makers, and only serves the purpose of getting a happy end.

Second, we don't even know for sure how the resets work (see here), i.e., how is it determined to what point in time does the reset go? If it really happens when he dies of an old age, will he loop back to his last sleep, to the helicopter, or somewhere in between?

There seems to be a general agreement that the reset goes to a point in time relevant to the death of the one resetting the time. But dying of an old age is inevitable, so where to reset to? IMO, the reset loses its purpose when it comes to the natural death, although one could argue (a big stretch, IMO) that the reset will go all the way to birth or early childhood, until he becomes a scientist that successfully researches immortality.

We have theories and guesses, but not a definite answer.

Yes...He got back the reset ability the moment he killed Omega & got covered in it's blood. He died before killing Omega. So when his body got covered in Omega's blood, the reset ability got transferred to him same like when he got covered in Alpha's blood at Verdun the very first time. So may be years later, when cage dies he can reset the day (for 24 hours). So he can live his last day once again. Eventually everyone dies at some point of time. He won't lose the reset ability unless he is injected with someone else's blood.

Infinitely? No. Assuming the Omega blood works like the Alpha blood, and the reset is to some fixed point in time, not length of time (the length varied from 24 to 48 or 72 hours, depending how long it took them to get through the beach to Germany), then he might loop a few times unconsciously, then a few more by choice. But not Infinitely.

Blood Loss without death will drain Cage of his powers, as it did Full Metal prior to him, and Cage when trying to escape General Dick. Statistically speaking, Cage will likely experience said Blood Loss event by accident on any given number of events.

Or Cage can cause it to happen on purpose. He knows the rules, he can use it to his advantage. Live a few life times then choose when to die. Infinity is a large number, Cage will likely get bored and commit suicide during some loop, when that loop is some number less than Infinity.