Windows 2.03 should run on it. Amstrad included it with their 2086 XT. Does your 1512 have an internal fan, I think the origional ones did not, but they were forced to add one due to overheating problems.
No, they weren't - they were forced to add a fan because the competition (which all had big PSUs in the system unit, unlike the Amstrads) convinced people it would be unreliable without one - FUD in action! My PC1512 doesn't have one and never gave a lick of trouble; my PC1640 had one, but I ended up disconnecting it when I powered it up recently because it was buggered and made an
awful racket.
(The PC1512/1640 are a bit weird in that the PSU is built into the monitor, which supplies power to the system unit - that way, the PSU electronics are in a relatively large airy space and cooled by convection. The downside is that if you want to upgrade the graphics, you need to keep the old monitor around…)
One similar rumour that
wasn't FUD was that the monitor could interfere with hard cards, like the one in the OP - I had no end of trouble with a Dysan model, which would randomly fail to locate sectors after much churning. Eventually I discovered that tilting the monitor forward a bit from the fully-back position fixed that right up, so that's something to be aware of; however, I believe later revisions included a metal ground shield inside the removable lid over the expansion slots, which might also address the problem.
Windows should run up to version 3.0 (which was the last version to support real mode), although one advantage the supplied GEM system will probably have over Windows (and most other graphical software of the era) is that it supports the 1512's weird '16-colour CGA' mode - 640x200x16 - which wasn't compatible with the EGA mode of the same specification. I don't remember ever seeing a PC1512 driver for Windows, but there might be one somewhere I guess...
If you wanted to update the supplied GEM/2 to the last DRI release, GEM/3, or the later GPLed versions such as FreeGEM (which restored functionality DRI had to remove after the Apple lawsuit), the driver is AMSTRAD.SYS in the GEMSYS directory on Disc 2 - but since the newer versions don't use ASSIGN.SYS to map devices to drivers, it needs to be renamed to something starting with SD before it'll be recognised. Alternatively John Elliott rebuilt it to conform to the later driver specification - see
http://www.seasip.info/Gem/Drivers/video.html - or his pages about the 1512/1640 at
http://www.seasip.info/AmstradXT/. Cliff Lawson also had some pages about the Amstrad machines, but since Murdoch's lot closed UK Online down they have to be found through the Wayback Machine at
http://web.archive.org/web/20100111065846/http://web.ukonline.co.uk/cliff.lawson/.Finally, if I remember in a couple of weeks when I get some long-delayed time off, I'll have a ferret through the boxes of accumulated Fine Old Hardware in the garage and see if I can dig out a spare 3Com EtherLink II - I don't want to give up the one I have in my 1512 at the moment, but there might be another floating around somewhere if it wouldn't be extortionately expensive to post.