Concerning the one listed as 5/8" for a Shopsmith. Could this be chucked into a three or four jaw lathe chuck?

You could, but you should not do that. It is designed to be screwed onto the same place your screw on your chuck.

How does this mandrel fit to the tail stock? Will I need an adapter for my tailstock? (I only have a center point)

The mandrel has to be fitted to the headstock and not the tailstock. It fits perfectly to a 3/4" x 16 TPI headstock drive.

Is there normally a little bit of slop in the brad point bit and 7mm brass tube that comes with the legacy kits?

The 7mm brass tube does fit in the blank loosely, but it seems to glue up okay. Don't forget to "scuff" up the tube prior to gluing with a light sanding. I only have the one bit and am just starting out myself, made 2 or 3 pens with no issues.

Where can i find just the extended length 7mm brad point drill bits?

Search Amazon for Frisch 7 mm brad point drill bit.

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Description

🖊️ Turn your pen projects from ordinary to extraordinary with precision and style!

VERSATILE COMPATIBILITY - Works flawlessly with PSI Woodworking mandrel savers and replacement shafts for expanded customization.
DURABLE METAL CONSTRUCTION - Built to last with premium metal materials ensuring long-term reliability and consistent performance.
COMPACT LIGHTWEIGHT DESIGN - At just 10.2 ounces and 10.2 inches long, it’s easy to handle and store without cluttering your workspace.
COMPLETE STARTER KIT INCLUDED - 7 bushings, knurled nut, and a sharp 7mm Brad Point drill bit to jumpstart your pen turning projects.
PRECISION THREADING FOR SEAMLESS ASSEMBLY - Screw-on mandrel pre-threaded to industry-standard 1" x 8 TPI for perfect fit every time.

The PKM-BL Screw-On Pen Mandrel by PSI Woodworking is a precision-engineered tool featuring a 1" x 8 TPI threaded shaft and a 7mm mandrel diameter. It includes seven 7mm bushings, a knurled nut, and a 7mm Brad Point drill bit, making it a complete starter kit for pen turning enthusiasts. Compatible with PSI mandrel savers and replacement shafts, this durable metal mandrel offers reliable performance and versatility for professional-quality wood pen crafting.

Specifications

Material	Metal
Cutting Diameter	7 Millimeters
Shank Type	Threaded
Brand	PSI Woodworking
Item dimensions L x W x H	10.2 x 1.7 x 1.7 inches
Tool Flute Type	Spiral
Point Style	Brad Point
Surface Recommendation	Wood
Number of Flutes	2
UPC	721782102835
Unit Count	1.0 Count
Global Trade Identification Number	00721782102835
Manufacturer	PSI Woodworking Products
Part Number	PKM-BL
Item Weight	10.2 ounces
Product Dimensions	10.2 x 1.7 x 1.7 inches
Item model number	PKM-BL
Is Discontinued By Manufacturer	No
Size	1" x 8tpi Screw-On
Item Package Quantity	1
Measurement System	Metric
Included Components	7mm Bushings(7), Drill Bit, Knurled Nut, Mandrel
Batteries Included?	No
Batteries Required?	No
Warranty Description	2 years under normal use

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