Can the U1525B accept an alkaline 9V battery (obviously without charging it)?
Yes, as I don't like the NimH cell for those 9V battery, as they're lousy and high self discharge.
It depends on the battery. The one that came with the meter does OK with holding a charge. I don't use my U1252B for prolonged measurements since I have bench meters for that, so I'm also in the "occasional use" category. The last time I charged the 8.4V battery was October, 2016. The battery level indicator currently shows about 70% charge remaining.
Addendum:
The battery mentioned above is a Powerex Imedion, 8.4V NiMH, 250mAh.
For my transistor tester, I got a Ray-o-vac Recharge Plus 8.4V NiMH, 200mAh. It was last recharged in October as well. Putting it in the U1252B, the battery level indicator shows 75% charge remaining.
Of course, this isn't a true test of the self-discharge rate. Just some anecdotal information.