What does this mean? Does this mean that if it passed 13.5 minutes already, one has to stop davening in the middle of S"E? Obviously this cannot be the case, and moreover there are opinions that b’dieved one can daven Mincha until 20 minutes after shkia, or even 58.5 minutes.

Shalom, Thank you for your comments. Whilst there are various opinions as to whether the Amidah of mincha must be finished before sunset, or if it is enough to just start the Amidah – ideally the Amidah should be finished before sunset. The Aruch HaShulchan rules that it is enough to start the Amidah before sunset, and he may be relied upon in times of need. Thank you for pointing out the unintentional lack of clarity in the answer. The 13.5 minuets refer to a widely accepted opinion (in Eretz Yisrael) that one may, in times of need, even start the Amidah up to 13.5 minuets after sunset. Blessings.