No Tpi and pitch of a ball screw won't match unless you have a really course screw.
The ebay seller you quoted is good and the most cost effective screws are 16 x 5 which means 16mm diameter by 5 mm pitch.

Whether or not it will fit in the space needed for the ballscrew is another matter but possibly will as some 3020'sdohave ball screws.

They will machine to suit the ends. However Chai now uses Fedex and you always now get hit for VAT plus a Fedex handling charge, usually 310.
Chai usually lies on cost so it drops the vat a touch but often the extra Fedex costs are equal to the goods, bear this in mind and possibly look to see replacing both X and Y at the same time or at least buy them both ?