So, to put it straight - is it perfectly okay to “touch” “pray” and get involved in prayers like we do when not in our period?
It is now, but, at least on paper, women were forbidden to receive communion while menstruating by custom or canon law from the earliest days until 1917, though it seems that that law was being ignored for some time before then. How long, I can’t determine.
And in about 1200, it seems that women were still forbidden to even enter a church while menstruating or after childbirth in some areas, as there is a letter by Pope Innocent III specifically stating that that custom had fallen out of use by that time in Rome.
Earlier, women, menstruating or not, were not allowed at all to be seen at all in church, but had to be hidden behind screens and curtains or up in balconies where the men couldn’t see them.
And yes, it had to do with biblical ritual purity, which became Christian tradition. And medieval prudishness, which was really extreme at times, even by Victorian standards.