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If one is wearing techeiles strings on his tallis katan, and goes up to be shliach tzibbur (lead the prayer), may he put on a shul tallis (prayer shawl) that is non-techeiles, i.e., all white strings? The reverse works as well (someone wearing all white strings puts on a garment with techeiles strings).
The reason I think it may be not allowed is due to the issue of tarti d'sasri, meaning a mutual contradiction.
I assume you mean the contradiction would be that your tzitis have tcheiles meaning your posek holds of that techeiles, whereas the tallis doesn't have tcheiles meaning whoever holds of it doesn't hold of tcheiles. Putting aside the debate on whether we know what tcheiles is or not, wearing tzitzis with and without tzitzis isn't inherently contadictory - tcheiles is an additional assay, so wearing one pair of tzitzis with and one without isn't a problem.
Yes, you can!
One example is Rav Belsky who only wore it on his tallit katan and never on his tallit gadol.
I guess it depends if you hold it is a chumrah/hiddur or a chiyuv.
If it is a chiyuv, then you can only wear techelet. See “Tekhelet in Tzitzit: A choice Mitzvah or an Absolute Obligation” by R Samuel Ariel.
If it is a chumrah or hiddur , then you can wear only white if you don’t have techelet in that moment or not enough money etc. See “The Definition of Nullifying a Mitzvah” by R Yehuda Rock.
Most people who start wearing techelet hold is a chumrah and do both at the same time for a while until they have enough money to fully switch to techelet.
