Is there any halachic basis for doing a chazi kedusha shemoneh esrei (where the chazan says out loud until kedushah, the kehillah answers kedushah and then the kehillah davens the silent shemoneh esrei? If so is it lechatchila or bedieved (for example, we have a work minyan where people are pressed for time and often want to conduct the minyan like this)?
Minchah Ketzarah (the shortened version of Minchah) should only be prayed when there is not sufficient time to pray the full Minchah prayer, i.e. close to sunset. Whenever there is sufficient time, the full Minchah should be prayed. The desire to “save time” does not justify the practice — even for the sake of Torah study.
Sources: See Beis Yosef (Orach Chaim 234) who quotes that the custom of Ashkenazim is to pray the full Minchah prayer (with chazaras hashatz), and that this is the correct custom, adding that a ban was pronounced in Tzefat against those who pray the shortened version. See also Magen Avraham (124:3) and Maamar Mordechai who rule similarly, and Kinyan Torah (vol. 3, no. 6) adds that it is wrong to daven the shortened version for the sake of Torah study (quoting from Chasam Sofer). Be’er Moshe (vol. 8, no. 106) writes that it is forbidden to daven the shortened version on a regular basis, and it is only permitted occassionally, under extenuating circumstances (quoting also from Radvaz, vol. 4, no. 165). Be’er Heitev adds that it is wrong al pi kaballah to daven the shortened version. However, see Aruch Hashulchan (232:6-7), who justifies using the shortened version (even on a regular basis) for a small minyan, in which there is concern that there will not be enough people responding “amen” to the blessings of the shaliach tzibbur. He adds that wherever possible, the full version should be used.