"...want to buy a #5Mk1..." Learn a bit about how to tell a real No. 5 from a fake. The quickest way to tell is if there is the manufacturer's name, lightening machining on the receiver and what sling swive lis on the butt stock. Canadian Arsenals, for example, didn't make 'em.
Go here for more and better info.
http://www.surplusrifle.com/no5/index.asp
1) Nope, any .303 British ammo will do nicely. You'll likely prefer a lighter bullet(like a 150) though. The felt recoil from a No. 5 is stout due to the lighter weight and that idiotic India rubber butt plate, laughingly called a recoil pad. A lighter bullet will help some.
2) Headspace is a manufacturing tolerance that allows any maker's ammo to be used in any like chambered rifle. If the headspace is excessive, the rifle is not safe to shoot. The
absolute worst case scenario is the lugs that keep the bolt closed breaking and the bolt coming back into your head. Far more likely is lots of case head separations leaving most of the case in the chamber(fixing that isn't terribly hard, but it sure is a nuisance), difficulty opening the bolt, blown primers and maybe the gases coming back after a case head separation and blowing out the mag.
Lee-Enfields of all models have a removeable bolt head. You have no idea if the existing bolt head is the original bolt head. The bolt head is changed in conjunction with headspace guages to adjust the headspace. Checking the headspace is not hard to do, but you need a No-Go and a Field guage to do it. They run $25 or $26 US each from Brownell's. One of the local smithies may have the guages and will check it for a nominal fee.
3) After shooting it. Every time.
4) Most of 'em require removing the rear sight. Brownell's sells one made by Cad-Technik that doesn't though. $75US. There's a link on the right side menu on the surplusrifles site. You may find one in one of your local gun shops though. Knew a guy who used a No. 5 for moose hunting for years with no scope.
Slug the bore too. Hammer a cast .30 calibre bullet or a suitably sized soft lead fishing sinker through the barrel and measure it with a micrometer. Lee-Enfield barrels can measure between .311" and .315" and still be considered ok. Larger than .315", the barrel is shot out. (Mind you, that doesn't happen often with a No. 5. Of the 500,000 made between 1943 and 1947, most didn't see much use.)