dado

are you asking for the hebrew names of g-d one might have heard in conversation? there are many of them - adonai, shammai, elohim, eloheinu is a partial list that (i believe) was in use prior to the period you mentioned. how to use them correctly is a little complicated, best to call up a local yeshiva (or three, they vary!) for advice on that.

a sick baby is not supposed to be circumcised, the correct procedure is to delay until the baby is healthy no matter how long it takes. how well this was followed back then is probably not knowable. it should be noted historical circumcision was almost certainly much simpler than today's standard practice: little axe, stretch a bit of skin out over a block, and whack.

the mourning rituals are a little complex. a full term baby dying before the first month is out is supposed to receive more or less full burial ritual, the ritual being dependant on the community. a premature baby only received the rituals if it survived the full 30 days, otherwise it was essentially classed as a miscarriage. the "30 day" magic number is almost certainly a relatively modern definition, in that era the period would probably have been based on number of shabbats or the lunar cycle.

a miscarriage was supposed to be treated by the community as a serious illness of the mother, not the death of a child, since classical judaism accepted the ethicality of abortion under (at least) some conditions.

there may be a difference depending on circumstances of birth. but you are conflating two separate issues: the child will have a name as soon as the parents decide it has a name, what happens on circumcision day is the community ritual of the naming. think of it as an introduction to the community. if the baby died before the naming/snipping, but a burial service was called for, the child would have been named in the memorial according to the parents wishes.

regarding a pregnant mother attempting suicide...oh boy. there is no concensus on the issue today, very unlikely there would have been a consensus then, and if there was, we have no way of knowing about it.

all this is "to the best of my knowledge" type stuff, so rest assured i won't be offended by corrections!

dado

in general, the elaborate rituals with us today were non existent then. they no doubt sat something like shiva, but i doubt very much davidian jews lit yahrzeit candles.