[Rex]

Channel One died a month or so before Sky 3. Sky 3 actually had a set of branding which lasted I think a month before being replaced by PickTV which had a very similar ident. I presume they would have changed it at the same time but they did one of those 'Sky preview on Sky 3 weekends' (forget how they branded it now) in mid-Feb as part of their high profile launch of Sky Atlantic. Why they felt they couldn't do that on a channel not called 'Sky something' I don't know.

Channel One had been coasting since it lost the Virgin brand, it had gone back to being mostly content aggregated from across the Living TV Group (as it's forerunner Ftn mostly but not exclusively did). Commissions like 'Restaurant in our Living Room' were moved to Living. Challenge continued with minor tweaks to its branding and Freeview carriage largely as it had been for a few months before (i.e. not a lot going on) - it wasn't until the spring when new content began arriving, starting with TNA wrestling.

I can't think of what Channel One exclusive content made it over to Pick TV?

I doubt anything exclusive to Channel One made it to Pick, but some of Flextech's archive was given slots on the channel a year after it launched. 

Pick retained the one year to 18 month gap between a programme's first broadcast on Sky branded channels and their eventual showing on Pick, a practice kept from Sky3. The sci-fi afternoon slot that Virgin 1 heavily advertised was carried over to Pick. Really in the end it was the core elements of those old services that were consolidated into Sky's FTA channel.