PBA: The “to the exclusion of all others” was a Chumra of R’ Soloveitchik (his Lashon too). All of his Talmidim do that.
No one holds like R’ Henkin nowadays. We don’t assume that all reform people are Safek Mamzerim. Even those Batei Dinim that won’t deal with a situation of a reform person (because they’re scared to go against R’ Henkin) will always accept a marriage and children that were Kosher according to R’ Moshe in this.
Akuperma: No. The Kiddushin is only done with Kesef. The Badeken, Chuppah, and Yichud room are all for Nisuin. And the Nisuin was all done Al Da’as the initial Kiddushin. If there is no initial Kiddushin, there is no marriage.