from your description, just like my M10 –
you will / should see on the headstock an allen bolt at the front of the bearing clamp locations front and rear of spindle and in the clamp a slot filled with laminated shims or a solid shim. WHEN you have carried out the check I suggested by checking both front and rear spindle play and ONLY IF you confirm play in the bearings approaching 0.002 thou first try gently tightening the allen bolt 1/16 at a time.
If you cannot, (please do not start levering hard on this bolt) loosen off and remove the laminated shim pack and remove one of the 2 thou shim foils, replace shim pack and gently repeat the tightening process 1/16 turn at a time.
In case there is no shim pack, but just a solid shim, you will have to gently lap the shim by the amount of play you measure.
Please please please do not attempt to over tighten the adjustment allen key or attempt too large a thinning of the shim otherwise you will REPEAT WILL! snap the headstock bearing clamp and scrap your lathe headstock. You should aim to remove play but still have free turning by hand of the spindle. Following adjustment, monitor temperature of bearing clamp.
The wear you report on the bead is trivial. Again you don't quantify how tight the saddle gets – they all do tighten on beds that have been used. If you can still push the bed by hand up to the tailstock end all is OK (assuming gibs are properly adjusted – neither too loose AND ALSO not to tight)
Re bowing of the lead screw – forgot to say you may need to check adjust the nut position on the apron, but as you say it is small, you can do this later.
If the tailstock was significantly out, you would see the effect in deep holes of the drill flexing, so then check for coplanar motion in tailstock barrel vertically and horizontally
Please refer to copious material on web reference tailstock adjustments – it is not a trivial job, and to do well will take you a long wet sunday afternoon to get spot on, especially if you need to shim to be coplanar vertically,. In any case, this is the least significant dimension, so a tolerance of 2 thou between barrel in and out would be ok. Once you have got it right, you will never want have to adjust it again!
From the measurements you give, the work piece is being bowed which suggests the cutting action may not be quite right.
The finish issues described are more likely down to poor material, cutter, feeds and speeds, settings, nothing inherent the dimensional accuracy you report would lead to the finish issues – you don't ay what cutter, suggest you use accurately HSS to start with if not already using.
I see no significant problems with this lathe.