What do these abbreviations stand for? I have seen them beside the names of righteous females. Does it mean that she should have long life? What is the equivalent for males?
See p. 322 of this Google book. The Hebrew abbrevaiation is יבדל"א for males and תבדל"א for females.
Loose transliteration - TiBadel/YiBadel Lecha'im Arukhim meaning "May s/he live long, on the contrary".
The alternate version you mentioned (tblch"t) stands for the same, except that Arukhim is switched with Tovim, meaning "good life."
The expression is used when referring to a living male or female in the context of mentioning a deceased person. For example, at a speech, one might say, "We recall Aunt Esther, aleha Hashalom (peace be upon her). And we are thrilled to see Grandma Royza, tibadel lechaim Arukhim with us, here, today."