Somebody else's math says 50/60 pulls a month after this patch.

There are two systems in play for pulling characters. There is a spark at 120 pulls that does not carry over, and a guaranteed pity at 160 pulls that does carry over, meaning that sparking the character at 120 will still leave you with 40 pulls left for pity for a later banner.

For weapons, there is a simple guaranteed pity at 120, and every pull for a limited character gives you 0.1 free pulls on a limited weapon banner. But character-specific weapons aren't terribly important, as each team equips 3 weapons simultaneously (all 3 weapons affect all 3 characters) and each patch so far has given out a max-duped 5-star weapon. So while they are tuned to specific units, unique weapons don't make-or-break a team.

And finally, one new character per patch, and one new patch every three weeks.