How to download acrobat 9 and activate it on new system?

If it's a volume lucense the retail download won't help. You need to use the volume license download, via your account manager.

Assuming it's a retail license, that is. Not a volume or bundled product.

you can expect, at least, some compatibility problems and limitations with new os'es.  but the install files for non-enterprise:

Downloadable installation files available:

• Suites and Programs:    CC 2017 |  CC 2015.5 | CC 2015 | CC 2014 | CC | CS6 | CS5.5 | CS5 | CS4, CS4 Web Standard | CS3
• Acrobat:  DC, XI, X | X Suite | 9,8 | 9 pro extended exe,9 pro extended 7z  | 9 standard    | 8 standard
• Captivate:  9 | 8 | 7 | 6 | 5.5, 5 | 1
• Cold Fusion:  11, 10 | 9.0.2, 9.0.1, 9.0.0, 8.0.1, 8.0.0, 7.0, 6.1, 6.0, 5.0, 4.0
• Contribute:  CS5 | CS4, CS3 | 3,2
• FrameMaker:  12, 11, 10, 9, 8, 7.2
• Lightroom:    6.8| 5.7.1|  4.4 | 3.6
• Photoshop Elements:  15,14,13,12,11,10,9,8 | 9,8,7 win | 8 mac | 7 mac
• Premiere Elements:  15,14,13,12,11,10,9,8| 9, 8, 7 win | 8 mac | 7 mac

Download and installation help for Adobe links

Download and installation help for Prodesigntools links are listed on most linked pages.  They are critical; especially steps 1, 2 and 3.  If you click a link that does not have those steps listed, open a second window using the Lightroom 3 link to see those 'Important Instructions'.