Must one stand up for someone who turned seventy years old since he is now a "saivo"? Does another person who is also over seventy have to stand up for him? Does the gender of either party matter?
One must stand for someone who is seventy. Source: YD 244:1; see discussion.
Regarding a elderly person standing for another elderly person,the Aruch Hashulchan YD 244:9 brings the Tur who says וכתב עוד: דהכי מסתבר נמי בשני חכמים או שני זקנים, שאין אחד צריך לקום מפני חבירו, אלא יעשה לו הידור. עד כאן לשונו. one does not have to fully rise if he is also 70 but to one should rise slightly(Hidur) .
Regarding standing for a woman, Chacham Ovadia in Yechavei Daas 3:72 brings from many sources (Sefer Chassidim,Sefer Hachinuch,Tshuvos Geonim,also seems from the Rambam sefer hamitzvos and Shu"t Bais Yehuda) that a woman over 70 one has to stand up for them and he paskens it is a mitzvah(it seems like a safek d'orasia because other argue) to stand. If one has to stand for an elderly non Jewish woman see the footnote on page 229.
MiP’nei Seiva Takum VeHadarta P’nei Zakein--this is the Mitzvah to stand before one who has reached the age of 70 [some say 60] and to honor Talmidei Chachomim and stand before them, even if they are young. If one is older [70 or 60], one must rise before him even if he is not a scholar and even if the one rising is a Chochom who is young. In this case, one need not stand to full height, but can raise himself up enough to clearly demonstrate Kavod. On the other hand, one must stand up for one who is actually a Chochom (whatever the age) to full height when he reaches within 4 amos until he passes by completely. One must also give Kavod to his Rebbi, even if he has not gained most of his wisdom from the Rebbi. A Rebbi, may, however, forgive any honor due him. As part of this Mitzvah, we must recognize that it is a great sin to disgrace or disparage Chachomim or even to dislike them, and that one who disgraces a Chochom does not have a Chelek in Olam Habah. This Mitzvah applies to men and women alike.
Halachipedia writes amongst other items:
- There are some who try to justify a minhag of being lenient regarding standing for an elder and Talmid Chacham. 
The reference reads:
8 Shach 244:11 seems to say that the minhag is to stand only for an Av Bet Din or Rosh Yeshiva, but he leaves it as a tzarich iyun.
Rav Chaim Zonenfeld in Salmat Chaim YD 59-60 explains that the Shach doesn't mean that they uprooted a Deoraita but rather that the Talmidei Chachamim forgo the respect due to them. Rabbi Zonenfeld seems to say that this is not accepted as the Halacha but only a defense of the minhag. Similarly, Sh”t Yabia Omer YD 3:13 writes that one should certainly not rely on the assumption that Talmidei Chachamim are mochel.
Kavod VeHiddur p. 38 cites some who say that we assume that in general a Talmid Chacham is mochel. I personally heard from Rabbi Schachter that we assume a Talmid Chacham is mochel.
Regarding elders, Kavod VeHiddur p. 64 quotes Rav Elyashiv saying that the minhag has what to rely on, since we assume that elders forgo the respect due to them.
So, as often, things are not quite so clear.